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SEMICENTENNIAL  PUBLICATIONS 


OF    THE 


UNIVERSITY  OF  CALIFORNIA 


1868-1918 


UNIVERSITY    OF    CALIFORNIA    PUBLICATIONS 


PHILOSOPHY 


volu:mk  :{ 


UNIVERSITY    OF    CALIFORNIA     PRESS 

BERKELEY 

1918 


FOOTNOTES 

TO 

FORMAL  LOGIC 


BY 

CHARLES    H.   RIEBER 


71 


CONTENTS 

PAGE 


I'KEFACE 


CHAl'TEK   I 

^^0»KR^'    rXDICTMKNT   OF    FoKMAl,   T>()(ilC    8 

CHAl'TKK  H 

ApPREHENSIOX,    (^UE.STIOX     AND    As.SERTIOX    34 — 

CHAPTER  III 
The  Import  ok  .IriMiMEXT  46 

CHAPTER  IV 

NeGATIOX  and  the   IXEIXITE  JUDGMENT  68 

CHAl'TEK  V 
Nature  of  Inference  81 

CHAPTER  VI 

Fm  MEDIATE    JXFERENCE 103    , 

CHAPTER  VII 
The  Case  Against  the  Syllogism 122 

CHAl'TER  VIll 

NOVELTV   AND   IDENTITY    IX   INFERENCE   147 


PREFACE 

The  psychologist,  on  the  one  hand,   and   tin-   metaphysician 
and  the  episteniologi.st,  on  the  othei-,  have  crowded  our  present 
\j  day  discussions  in  tlie  fiekl  of  pure  logic  into  a  very  narrow  and 

^  uneoinfortable  i)osition.     No  sooner  does  the  logician   raise  the 

v)  (luestion  as  to  the  origin  and  nature  of  the  thinking  process, 

^x         than  the  psychologist  warns  him  that  he  is  trespassing  in  fields 
not  his.     Especially  is  tliis  true  when  we  venture  to  discuss  such 
^  (piestions  as  the  process  wliei'ehy  judgment  develops  into  infer- 

V  ence  or  is  tlcjiressed  into  eoncej)tion.     Tliis  we  are  told  is  not 

^  logic,   but   genetic   psychology.     On   the   otlun-   hand,   when   the 

1^  logician  raises  the  (juestion  as  to  the  nature  of  knowledge  in  gen- 

v^  eral,  he  is  again  i-el)uked  foi-  passing  into  the  domain  of  iiieta- 

physics,  epistemology  or  ontology.     It  has  been  said  tluit  if  the 
^  logician  should  accept  these  I'estrictions  which  his  neighbors  have 

^  imi)ose(l  upon  his  field,  there  would  be  little  left  of  logic,  except 

Sj         a  mere  collection  of  misleading  formulae  coui)led  with  a  little  ele- 
mentary grammar. 

I  think  the  situation  is  not  (juite  so  desi)erate  as  this,  and  1 
hope  in  some  small  measure  in  thest-  studies  to  justify  the  present 
tendency  to  widen  the  field  of  logic.  When  we  attempt  to  define 
the  nature  and  scope  of  logic,  or  of  any  other  of  the  philosophical 
sciences,  we  find  our  iiujuiries  passing  by  imperceptible  steps 
from  one  field  to  anothei'  until  presently  eaeli  subject  in  tui-ii 
claims  to  be  the  whole  of  philosophy.  I  believe  it  to  be  a  mis- 
take to  divorce  logic — even  for  educational  purposes — from  the 
other  philosophical  sciences.  I  do  not  see  how  it  is  possible  to 
answer  the  questions  that  are  more  than  ever  today  hesetting 
logical  doctrine  until  we  have  first  settled  some  of  the  funda- 
mental problems  of  philosophy.     Formal  Logic  is  again  on  trial 


6  FOOTNOTES  TO  FOBMAL  LOGIC 

for  its  life.  In  recent  years,  at  least  four*  important  volumes 
have  been  entirely  devoted  to  this  modern  indictment  of  tradi- 
tional logic.  Having  now  for  some  fifteen  years  been  charged 
with  the  responsibility  of  teaching  Formal  Logic,  and  to  more 
than  half  a  thousand  students  each  year,  I  feel  morally  neces- 
sitated, as  one  of  the  humblest  of  the  disciples  of  Aristotle,  to 
give  some  justification  for  the  faith  that  is  in  me. 

In  the  introductory  pages  of  his  Formal  Logic,  Professor 
Schiller  remarks,  in  a  somewdiat  disheartened  mood,  "it  is  not 
unlikely  that  this  whole  revolt  will  come  to  nothing  and  that 
Logic  will  continue  to  be  taught  on  the  traditional  lines."  He 
takes  comfort,  however,  in  the  belief  that  the  failure  of  the 
reform  movement  will  not  be  due  to  any  intrinsic  error  or  weak- 
ness in  the  movement  itself,  but  to  the  fact  that  the  prestige  of 
tradition  is  so  overwhelming,  the  force  of  habit  so  insidious. 
Dr.  Mercier  in  the  preface  to  his  New  Logic  also  expresses  gloomy 
misgivings  as  to  the  fate  of  his  volume.  He  says  "by  the  time 
the  New  Logic  has  stood  two  thousand  years  ...  no  doubt  it 
will  have  had  all  the  guts  taken  out  of  it."'  I  think,  however, 
that  no  serious  attempt  w^ill  be  made  to  disembowel  his  book.  Dr. 
Mercier  has  been  disappointed,  so  he  says,  that  none  of  the  older 
writers,  Bosanquet,  for  instance,  have  replied  to  his  criticisms. 
It  seems  more  likely  therefore,  that  his  volume  will  be  allowed 
to  dry  up  with  its  entrails  in  it  and  become  an  interesting  object 
for  antiquarian  research  in  the  generations  to  come. 

I  have  chosen  the  title  Footnotes  to  Formal  Logic  for  these 
studies,  rather  than  the  more  pretentious  title  Logical  Theory,  or 
Principles  of  Logic,  in  order  that  I  might  convey  my  own  con- 
sciousness of  their  incompleteness  and  shortcomings.  But,  while 
the  collection  of  essays  is  by  the  title  confessed  to  be  fragmentary, 
I  hope  I  have  made  plain  a  thread  of  continuity  running  through 
them  all.     I  have  not  attempted  to  present  a  brief  for  Formal 


*  Schiller,  F.  C.  S.,  Formal  Logic,  London,  Macmillan,  1912;  Sidg^vick, 
A.,  Elementary  Logic,  Cambridge,  University  Press,  1914;  Dewey,  John, 
Essays  in  Experimental  Logic,  Chicago,  University  of  Chicago  Press,  1916; 
Mercier,  Charles,  A  New  Logic,  Chicago,  Open  Court,  1912. 


FEE FACE  7 

Logic  tliat  is  witliout  (jualiiication  ;  I'or  1  have  at  times  said  soim- 
severe  things  about  the  ancient  system.  However,  I  think  on  thi- 
whole  my  efforts  will  be  regarded  as  a  defense  of  the  Traditional 
Logic,  and  to  that  I  shall  not  object.  For,  to  use  a  very  apt 
phrase  of  Dr.  ]\Iercier,  if  I  have  to  choose  between  the  New  Logic 
and  tlie  Old  Logic,  I  should  "i)lum])  for"  tlie  latter. 


CHAPTEE  I 
THE  MODERN  INDICTMENT  OF  FORMAL  LOGIC 

I. 

The  new  theories  of  thought  all  make  a  common  criticism 
upon  the  old  idealistic  Formal  Logic.  Whether  we  call  these 
modern  theories  of  knowledge  pragmatic,  realistic  or  empirical, 
matters  little  for  our  present  purpose.  They  all  agree  in  saying 
that  the  conceptual,  a  priori  logic  has  never  undertaken  to  set 
forth  the  conditions  out  of  which  actual  thought  has  arisen  :  nor 
has  it  defined  the  principles  that  estimate  the  success  of  thought  "s 
accomplishments.  It  has  no  theory  of  the  whoncr  and  the 
whither  of  thought.  "What  we  have  to  reckon  with,"  Professor 
Dewej^  writes,  "is  not  the  problem  of  How  can  I  think  ilhrr- 
hauptf  but  How  shall  I  think  right  Jxre  and  nov?  not  what  is 
the  test  of  thought  at  large,  but  what  validates  and  confirms  ihk 
thought.  "1 

I  wish  to  submit  at  once,  and  it  will  be  one  of  the  central  con- 
tentions of  these  studies  that  it  is  unfair  to  the  formal  logician, 
even  of  the  old  orthodox  type,  to  say  that  he  is  unwilling  to  take 
notice  of  the  concrete  facts,  that  he  has  a  contempt  for  the  parti- 
culars, that  the  universals  are  more  precious  to  him  than  the 
particular  cases  to  which  they  apply.  Only  a  hasty  and  reckless 
idealist  affirms  any  such  doctrine.  An  essential  part  of  thought 
is  always  engaged  in  the  effort  to  reach  final  truths — propositions 
that  are  not  merely  finally  true  in  the  sense  of  being  a  complete 
and  adequate  adjustment  to  an  innnediate  situation,  but  truths 
that  are  certain  and  universally  valid.  Even  the  most  zealous 
defender  of  the  modern  "flowing  philosophy''  admits  the  exist- 
ence of  this  logic  iihrrhaupt,  albeit,  he  insists  that  it  is  a  useless 


^  Siudies  in   Lopical  Theory   (University  of  Chicago  Press,   1903),  p.  3. 

[8] 


riih:  M(H>i:i;s  isdictm i-:sr  of  hon.M m.  ijx.ic  i) 

pursuit.  Another  part  of  thought,  which  regards  itself  just  as 
essential,  attempts  to  arrive  at  praetieal  truth  ;  it  is  concerned 
with  the  I'cconst  I'lict  idii  (if  \\\r  ' "  iiiinniliate  situation.""  Now. 
p].\periniental  Logic  a.ssei'ts  its  competency  to  i)ass  judgment  not 
only  upon  its  own  pragmatic  pi-ocess,  but  also  upon  the  episte- 
inological  aspirations  of  the  Real  Logic.  And  it  is  to  this  basic 
doctrine  of  the  new  scliool  tlia1  the  old  scliool  registei-s  its  earnest 
caveat. 

The  idealism  represented  in  tliese  pages  is  of  a  very  old- 
fashioned  t^'pe.  It  essays  to  defend  even  so  abstract  an  idealist 
as  Plato  against  the  {assaults  of  the  modern  realist.-  It  has  often 
been  said  that  the  logic  of  Platonism,  or  any  absolute  idealism, 
drives  one  either  to  pure  intellectualism  or  to  pure  mysticism. 
But  even  Plato  did  not  j)ut  the  whole  emphasis  in  his  thinking 
on  the  theory  of  knowledge.  Piiilosophy  was  for  him,  to  be  sure, 
primarily  a  discipline  of  the  mind ;  but  it  was  a  discipline  which 
ended  always  in  the  service  of  action;  it  was  the  propaedeutic 
foi-  character.  Thought  was  quite  as  pragmatic  for  Plato  as  it  is 
for  any  of  the  modern  voluntarists,  only  it  was  pragmatic,  1 
should  say,  in  a  thoroughly  defensible  sense.  The  mind's  essential 
nature  is  exhibited  in  its  everlasting  aspiration  after  truth.  Put 
perfect  insight,  genuine  wisdom,  has  as  its  essential  characteristic 
the  inevitable  necessity  of  expressing  itself.  The  knowledge  tha'. 
th(>  mind  wins  nuist  tlow  out  into  character.  Man's  complete  life 
consists  not  only  in  thinking  perfect  thoughts,  working  them  out 
like  nuggets  of  gold,  but  also  in  coining  them  into  action.  Plato 
insisted  always  that  Logic  is  the  absolutely  indisjiensable  pre- 
rerpiisite  of  Ethics,  and,  conversely,  that  Ethics  was  the  inevitable 
outcome  of  Logic. 


-  In  these  studies  I  shall  often  speak  of  instiunientalism,  realism,  and 
pniffuiatisni  as  if  they  were  identical  doctrines.  I  am,  of  course,  fully 
aware  of  the  several  points  of  vital  difference  which  have  been  insisted 
upon  by  various  members  of  the  two  schools.  But  for  the  purpose  of  the 
contrast  with  idealism  we  may  nejjlect  tht\se  differences  and  deal  with  their 
central  agreenu'nt.  Botli  realism  and  instrumentalism  declare  that  think- 
ing is  instrumental  oi'  reconstructive  and  not  constructive,  as  idealism 
always  professes.  They  liold  that  tlioufilit  finds  real  brute  existences  in 
the  world  of  ])resented  fact — structures  tluit  are  not  created  but  discovered. 


10  FOOTNOTES  TO  FOliMAL  LOGIC 

Logic  in  the  fullest  sense  of  the  word  is  therefore  the  source, 
but  not  the  final  goal  of  the  Platonic  philosophy,  or  of  any  serious 
idealism.  Insight  is  not  for  its  own  sake  but  for  the  sake  of  action. 
Knowledge  turns  not  inward  upon  itself,  but  outward  upon  con- 
duct. It  is  practical ;  it  is  pragmatic.  According  to  the  sublime 
Platonic  formula  of  life  (even  in  its  most  modern  interpretation 
by  Caird,  Koyce,  Howison  and  others),  knowledge  is  virtue,  not, 
knowledge  is  knowledge.  Plato  would  have  agreed  entirely  with 
a  modern  up-to-date  metaphorical  epigram;  "knowledge  that 
turns  inward  upon  itself  creates  a  current  so  hot  that  it  burns 
out  the  fuse." 

Knowledge  begins  with  surprise  and  ends  in  the  rational  dis- 
sipation of  surprise ;  it  is  original,  under ived,  reminiscent.  This 
is  the  basic  doctrine  of  Plato's  philosophy  which  has  been  echoed 
and  reechoed  through  twenty-three  centuries  of  idealism.  But 
now  we  must  bear  in  mind  that  it  is  not  pure  wonder,  just  un- 
alloyed surprise,  but  rather  a  troubled  wonder  that  is  the  source 
of  knowledge.  We  are  not  and  cannot  be  just  the  passive  happy 
spectators  of  a  stream  of  fugitive  impressions  flitting  across  the 
stage  of  consciousness.  The  presentations  from  the  sense  world 
come  as  competing  alternatives.  This  it  is  very  important  to 
remember  in  considering  any  conceptual  logic.  The  Platonic  con- 
ception of  wonder  has  lent  itself  to  poetic  imagination  and  strik- 
ing rhetoric,  but  it  is  a  misunderstanding  of  it  that  makes  it  syn- 
onomous  with  pure  reverie,  mystic  contemplation.  Consciousness 
is  not  merely  passive,  it  is  essentially  active.  All  waking  con- 
sciousness is  one  continuous  affirmation,  an  affirmation  which, 
to  be  sure,  always  expresses  itself  in  a  disjunctive  judgment, 
as  we  shall  see  later.  Now  Plato  insisted — at  times  with  almost 
indignant  emphasis — that  sense  presentations  are  incapable  of 
thickening  up  into  any  final  meaning,  or  validity  of  their  own. 
Objects  of  sense  perception  are  always  particulars.  And  no 
accumulation  of  particulars  by  sheer  juxtaposition  or  association 
can  yield  true  knowledge.     An  aggregate  of  particulars  is  just 


'/■///•;  M()i>i:i:s  isdictmest  or  formal  lock:  ii 

anollier  particular.  Kuowledj^L'  presupposes  universals.  Tliere 
is,  therefore,  a  world  of  ideas  above  this  world  of  fleeting  sense 
perception.  And  llic  nid-e  beginner  in  tlic  study  of  Platonic 
phiIosoi)]iy  knows  tliat  tlie  ideas  are  entities,  genuine  objects  of 
knowledge,  and  that  tliey  nuist  never  be  taken  as  states  of  con- 
sciousness merely. 

The  New  Logic  cancels  the  distinction  between  origin  and 
validity,  between  what  we  discover  about  a  particular  fact  through 
an  analysis  of  its  present  content,  and  what  we  learn  about  it  by 
an  historical  study  of  tlu-  conditions  of  its  l)irtli  and  development. 
Professor  Dewey^  says  of  the  oi-tliodox  logieian  :  "He  deals  with 
the  question  of  the  eternal  nature  of  thought  and  its  eternal 
validity  in  relation  to  an  eternal  reality.  He  is  concerned,  not 
with  genesis,  but  with  value,  not  with  a  historic  cycle,  but  with 
absolute  distinctions  and  relations";  and  again:  "We  have  no 
choice  save  either  to  conceive  of  thinking  as  a  response  to  a  specific 
stimulus,  or  else  to  regard  it  as  something  'in  itself,'  having 
just  in  and  of  itself  certain  traits,  elements,  and  laws.  If  Ave 
give  up  the  last  view,  we  must  take  the  former." 

It  is  an  engaging  and  important  question  which  instrumental 
Logic  asks,  How  does  empii'ieal  science  come  by  its  general 
principles,  and  particularly  how  does  it  prove  them  ?  But  the 
idealistic  Logic  has  always  insisted  that  this  is  not  the  same  as 
the  determination  of  the  principles  of  knowledge.  If  the  New 
Logic  intends  merely  to  assert  that  we  never  reach  a  conclusion 
unless  we  have  already  come  by  it  through  experience,  no  idealist 
will  take  exception.  Thei-e  is  a  deep  truth  in  the  assertion  that 
we  believe  first  and  i)rove  afterward  or  not  at  all.  AVe  do  not 
know  because  we  have  reasoned  but  we  reason  because  we  know. 
Kant  was  very  explicit  on  this  i)oint.  He  says,  "Logic,  on  the 
contrary,  being  the  general  propaedeutic  of  every  use  of  the 
undei'standing  and  of  the  reason,  can  not  meddle  with  the 
sciences,   and   anticipate   their  mattei-,   and  is  therefore  only   a 


3  Studies  ill  Logical  Tlu-oi-.v,  ]•.   14. 


12  FOOTNOTES  TO  FOUMAL  LOdlC 

universal  Art  of  Biasoti,  the  art  of  making  any  branch  of  knowl- 
edge accord  with  the  form  of  the  understanding.  Only  so  far 
can  it  be  called  an  organon,  one  which  serves  not  for  the  enlarge- 
ment, but  only  for  the  criticism  (nul  correction  of  our  knowl- 
edge.''* 

I  need  only  refer  to  a  significant  fact  that  has  been  pointed 
out  frequently,  nanu^ly,  that  several  different  meanings — some  of 
them  quite  diametrically  opposed — have  been  given  to  the  term 
"practical"  as  applied  to  judgment.  Even  the  pragmatists  who 
may  now  be  said  to  have  appropriated  to  themselves  the  "trade 
mark"  of  the  term  practical,  seem  to  differ  widely  in  their 
definition  of  it.  In  Kant's  distinction  between  theoretical  and 
practical  reason,  the  tlieoretical  reason  is  always  practical,  or 
pragmatic,  although  certainly  not  in  the  sense  in  which  the  word 
is  employed  in  some  of  the  recent  theories  of  judgment.  When 
the  pragmatist  declares  that  all  judgments  are  practical,  does 
he  mean  to  assert  that  the  object  of  the  judgment  is  created  in 
the  act  of  judging '.  The  question  as  to  precisely  what  the 
expression  "creates  its  own  object"  may  mean — the  question 
upon  the  answer  to  which  depend  so  many  vital  issues  in  Logic — 
will  be  considered  more  fully  in  a  later  cliaptt-r  in  dealing  with 
the  postulated  objectivity  in  thought.  1  wisli  only  to  say,  in 
passing,  that  this  creative  activity  is  the  essence  of  all  the 
alleged  theoretical  judgments  in  any  type  of  idealism,  even  the 
niost  ancient.  The  primary  object  of  the  Critique  of  tlie  Pure 
Reason  was  to  show  that  thought  does  actually  create  its  object : 
or,  the  least  we  may  say,  is  that  it  assists  in  its  creation,  in  so 
far  as  it  supplies  the  form  tliat  matter  must  take  in  knowledge. 

Any  Logic  that  regards  all  judgments  as  practical  labors 
under  this  inherent  difficulty.  How  can  any  concrete,  particular 
instance  of  knowing  hope,  at  one  and  the  same  time,  to  create  a 
valuable  object  and  to  knou-  its  creation  as  valuable.  I  am 
restating,  I  know,   a   vei-y   fanuliar  and  old   criticism  of  prag- 


■i  Introduction    to   Lntilc;   translated   by   T.   H.    AUliott    (London,   Long- 
mans, 1885),  p.  3. 


THE  MODF.US  I S DICTM EST  OF  /■OHM. 11.  I.OCIC  V.'. 

iiiatisiii  wlicii  1  sa\'  tliat  value  caiiuot  he  r('};ai'(l<'(l  as  tin-  liiddi'H 
wortli  within  a  situation,  wiiicli  needs  oidy  to  he  hi-ouj^^lit  to  lif^ht, 
or  evaluated.  \'ahie  is  not  the  seli'-ch'tei'iiiined  issue  of  facts. 
Value  proceeds  fi'oni  tlie  activity  which  i-elates  particular  to 
universal,  fact  to  law.  The  world  of  value  is  Ix^vond-  the  woi-ld 
of  fact  in  the  same  s<'nse  that  tlie  sti-aij^lit  line  i.s  heyond  the  eurve 
wliich  it  detei-niines. 

Pragmatic  logicians  arc  over-fiMed  with  the  spirit  of  initural 
science.  Tins  they  say,  begins  with  pi-actieal  definitions  and 
follows  practical  metliods  to  practical  conclusions.  Natural 
science  has  come  to  have  such  an  enormous  place  in  the  common 
life,  as  well  as  in  the  academic  world,  tiiat  we  can  readily  see 
how  tlie  New  Logic  has  come  by  its  ovei'-weaning  sense  of  the 
im])ortance  and  cei'tainty  of  the  scientific  method.  The  enthu- 
siastic devotees  of  natural  science  easily  win  the  approbation 
pf  the  fickle  public,  when  the}'  contrast  the  definite  advance 
which  the  so-called  i)ragmatic  sciences  have  nuide,  with  the  con- 
fusion and  dispute  which  we  seem  still  to  find  in  the  world  of 
speculative  Logic.  The  experimental  logician  insists  that  the 
difficulty  with  all  the  philosophical  sciences — and  not  less  so 
with  Logic  than  with  any  of  tlie  others — is  tliat  they  ai"e  all 
destitute  of  either  accurate,  initial  definitions  or  cei'tain  methods, 
foi"  the  solution  of  thi'ir  prol)lems.  The  analysis  and  tlie  evalua- 
tion of  judgments  of  prai-tice  without  extei'iial  points  of  orienta- 
tion would  be  as  difficult  as  the  determination  of  a  system  of 
conies  without  the  axes  of  reference.  The  conditions  of  asser- 
tion are  manifold — sometimes  operating  singly,  but  for  the  most 
part  combined  in  amazing  complexity. 

It  is  the  task  of  pi'actical  thought  (upon  this  point  the  idealist 
agrees  entirely  with  the  pragmatist)  to  determine  in  what  meas- 
ure each  of  the  antecedents  enters  into  the  joint  effect.  The 
difficulty  in  accom|)lisliing  tiiis  task  is  the  same  as  the  difficulty 
that  we  meet  elsewhere  in  the  inductive  sciences,  for  example,  in 
the  ai)plication  of  .Mill's  Method  of  Agreement.     Tiiere  the  plur- 


< 


14  FOOTNOTED  TO  FOBMAL  LOGIC 

alitv  of  causes  renders  the  causal  determination  uncertain.  And 
as  in  the  world  of  outer  natural  sciences  Ave  find  plurality  of 
causes  and  intermixture  of  effects  so  in  the  world  of  inner 
natural  science  we  discover  each  phenomenon  to  be  the  meeting- 
point  of  converging  strands  of  conditions  coming  out  of  the  past 
and  diverging  strands  of  effects  going  out  into  the  future.  They 
are  like  the  knots  in  a  net  into  which  and  from  which  various 
cords  run.  All  of  this  is  a  most  interesting  study  in  Psychology 
but  it  is  not  Logic.  How^ever  cleverly  phenomenena  may  be 
explained  as  the  cross-section  of  the  evolutional  series,  that  is, 
as  the  meeting-point  of  forces,  there  still  remains  to  be  explained 
the  essential  identity  or  form  of  the  whole. 

II 

Every  act  of  thought  is  in  the  first  instance  an  immediate 
presence,  but  it  is  also  embedded  in  a  continuum.  This  con- 
tinuum, in  its  entirety,  is  reality.  It  includes  the  present  think- 
ing, and  it  is  or  may  be  the  object  of  that  present  thinking.  We 
have  illustrated  here  the  axiom  of  higher  mathematics  that  the 
part  can  be  put  into  a  one  to  one  correspondence  with  the  whole 
of  which  it  is  a  geimine  part.  On  this  point  I  should  differ  from 
Professor  Dewey  in  the  central  thesis  of  his  system  that  ''think- 
ing is  set  in  a  continuum  which  is  not  an  object  of  thought."^ 
On  the  view  which  I  am  presenting  it  is  evident  that  the  term 
reality  is  not  so  ' '  particularly  treacherous. ' '  as  Professor  Dewey 
thinks.  There  is  no  contradiction  in  its  two  uses — as  a  term  of 
indefinite  reference  and  as  a  term  of  discriminate  reference. 
The  part  of  the  continuum  which  is  out  of  sight  and  is,  there- 
fore, not  an  object  of  thought  is  in  the  instrumental  view,  never- 
theless, always  suggested  by  the  present  thinking.  Now  the  dif- 
ference between  the  idealistic  and  the  instrumental  theory  of 
judgment  hinges  upon  the  meaning  of  the  word  suggest.  The 
instrumentalist  says  that  this  suggested  aspect  of  the  continuum 


5  Experimental  Logic,  p.  10. 


rilF.  M()l)l:i:S  IS DICTMEST  Oh'  FORMA  I.  LOGIC  15 

is  never  a  part  oi'  the  yivcn;  tlic  idealist  insists  that  tin.'  sug- 
gested  fact  is  already  in  a  profound  sense  a  present  fact,  other-  -^  {'K^ 
wise  it  would  not  be_eYen  suggested.  Idealism  provides,  without 
contradiction,  for  both  the  discrete  and  the  continuous  aspect  of 
tile  whoh'  within  wliicli  ])r('S('nt  thinking  is  set.  Bradley  and 
liis  l'olh)\V('i\s.  in  iniikitiL;'  i'c;ilily  llic  iilt  iiiuitc  siihjcct  in  judg- 
ment have  kept  in  mind  these  two  uses  of  the  word." 

Moreover,  I  can  not  think  it  wholly  just  to  the  traditional 
theories  of  knowledge  to  say  with  Professor  Dewey  that  they 
were  concerned  entirely  with  tlie  "question  of  the  etei-nal  nature 
of  thought  and  its  eternal  validity  in  relation  to  an  eternal 
reality — that  tliey  were  engaged,  not  witli  the  genesis  but  with 
value,  not  with  a  historic  cycle,  but  with  absolute  distinctions 
and  relations."'  Tlie  old  ])re-I)arwinian  metaphysics  did  not 
ignore  the  (luestion  of  genesis,  but  it  saw  tluit  all  historical  ques- 
tions are  at  last  (le])endent  upon  (piestions  of  value,  upon  abso- 
lute distinetions.  Even  Plato  recognized  the  fact  that  trutli 
and  falsity  were  organically  related  to  practical  life,  to  action, 
to  the  very  needs  in  concrete  experience  upon  which  the  logic 
of  pragmatism  lays  such  emphasis.  And  it  is  not  attri])uting  to 
Plato  doctrines  that  are  not  his,  to  say,  in  the  terminology  of 
the  new  theory,  that  he  did  not  teach  that  truth  and  falsity  should 
be  wholly  divorced  fi-om  the  jiarticular  activities  that  we  perform 
at  a  specific  need.  But  he  would  re])ly  to  the  pragmatists 
today  in  the  sj)irit  of  liis  reply  to  the  so])hists.  "The  construc- 
tions of  these  specitic  activities  ai-e  not  true  unless  they  conform 
not  only  to  the  intra-temporal  is  but  to  the  supra-temporal 
ought." 

Professor  Schiller  asks  the  logician  of  the  old  school  a  simple 
question  which  he  rightly  says  cannot  be  shirked:  "When  he 
asserts  what  seems  to  him  a  truth  does  he  take  any  steps  to  ascer- 


cBosanquet  says:  "The  subject  in  every  jiuljjmcut  of  Perception  is 
some  given  spot  or  point  in  sensuous  contact  with  the  percipient  self.  But 
as  all  reality  is  continuous,  the  subject  is  not  merchj  this  given  spot  or 
point."     Lofjic  (etl.  2;  Oxfonl,  Clarontlon  Press.  1011),  T,  78. 

"  Logical  Thcori/,  p.  14. 


16  FOOTNOTED  TO  FOL'MAL  LOGIC 

tain  whether  or  not  it  is  'objective,'  and  whethei-  other  men 
(all  or  any)  agree  with  him?  If  he  does,  what  are  they  and 
what  is  their  logical  value?  If  he  does  not,  why  should  not  his 
claim  be  treated  as  a  random  one?"**  But  now  this  is  precisely 
the  question  which  a  score  of  critics  have  been  asking  the  prag- 
matist  for  the  last  two  decades.  In  an  essay  on  "Pragmatism 
and  the  a  priori"  printed  in  1905,  I  said: 

A  judgment  must  be  more  than  a  mere  effort  to  reconstruct  the  situa- 
tion in  which  we  find  ourselves  from  moment  to  moment;  so  much  is,  of 
course,  the  first  condition  it  must  fulfil.  But  in  addition  to  being  a  suc- 
cessful present  response,  it  must  be  true.  This  requires  that  it  not  only 
conform  to  a  passing  is,  but  to  a  permanent  ought.  Each  judgment  of  mine 
is,  in  one  aspect,  my  response  to  a  present  situation.  But  before  I  am 
entitled  to  call  it  true,  I  must  know  why  the  response  has  been  what  it  is; 
that  is,  I  must  be  able  to  say  that  another  than  myself  would  have  responded 
to  the  situation  in  precisely  the  same  way. 

Experimental  Logic  tells  us  that  we  must  take  all  of  our 
problems,  logical,  ethical,  and  even  religious,  to  experience  for 
solution.  We  must  let  the  particular  concrete  facts  of  sense 
experience  tell  their  story.  But  the  result  is,  as  I  have  tried  to 
point  out,  experience  has  in  the  end  no  necessary  story  to  tell. 
Did  not  Hume  prove  that  once  for  all?  If  we  follow  the  realist 
far  enough,  as  he  lets  facts  recite  their  tale  of  explanation,  he 
invariably  brings  us  back  to  the  point  from  which  he  set  out. 
He  displays  a  remarkable  combination  of  true  insight,  with  what 
seem  inexcusable  lapses  from  reason  in  his  empirical  explana- 
tions. These  modern  apostles  of  the  "flowing  philosophy,"  are 
standing  upon  a  platform  from  under  which  all  support  has  been 
taken.  The  pragmatist  proceeds  with  liis  empirical  test  for  truth 
paying  no  heed  to  the  constant  protest  of  tlie  idealist  against 
the  circular  reasoning  that  is  involved  in  any  attempt  to  make 
experience  self-explanatory.  To  the  idealist's  question,  How 
do  you  explain  the  contradiction  in  experience?  he  replies 
naively,  "There  are  no  contradictions."    Of  course  no  contradic- 


sMiiul,  n.  s.  XV  in   (1909),  402. 


THE  M()i>r:i:.\  ixdktm  i:\r  of  f<)i;.m.\l  loc.ic  i: 

tioii  will  ever  he  discovcrtMl   in  cxpiTii'iicc  if  lir  test  ('xj)(M-i«'nce 
by  itself. 

The  (liri'ci-ciicc  between  the  idealistic  and  the  |)ra<ruiatic  intef- 
pi'ctation  of  cxpcricnct'  is  to  be  found  in  tlic  way  in  which  each 
of  tilt'  two  schools  reads  off  the  relationship  between  external 
and  internal  meaning.  For  the  idealist  tlie  whole  problem  of 
knowledge  rediiees  itself  to  the  (|U('stion.  How  arc  priniai-y  or 
intei-nal  meanings  of  itleas  related  to  theii"  secondary  oi'  appar- 
ently extei-nal  meanings?  For  the  i-ealist,  the  i)ragmatist,  and 
in  fact  for  evei-y  type  of  positivist,  the  (|uestion  is,  How  ai'e  the 
brute  facts  of  the  primary  objective  reality  related  to  the  second- 
ary apparently  internal  meanings  which  we  call  ideas?  If  experi- 
ence be  taken  in  a  wide  sense  as  synonomous  with  the  entire  con- 
tent of  consciousness,  and  thus  iiuide  to  cover  both  the  active 
as  well  as  the  passive  aspects  of  thought,  then  of  coui'se  the 
idealist  would  agree  with  the  empiricist  that  the  laws  of  thought, 
as  w'ell  as  the  laws  of  existence  come  from  experience. 

Ill 

The  critics  of  Formal  Logic  have  failed,  I  venture  to  tlniik. 
to  distinguish  between  the  thought  form  and  the  language  form 
in  which  that  thought  form  expresses  itself.  The  two  are  not 
the  same ;  and  Fonnal  Logic  deals  with  form  in  the  first,  not 
the  second  sense.  Professor  Sidgwick  says,  "Preoccupied  as 
Logic  has  chosen  to  be  with  forms  of  statement,  it  cannot  wholly 
desert  the  idea  that  the  meaning  of  a  statement  is  something  that 
belongs  to  its  form,  instead  of  the  form  being  a  more  or  less 
successful  attempt  on  the  part  of  a  speaker  to  express  a  mean- 
ing."" Not  all  teachers  of  Fornud  Logic,  1  am  sure,  would  agree 
with  this  statement.  The  ti'anslation  of  the  literary  or  rhetorical 
forms  of  statements  into  the  logical  foi'iu  of  thought,  is  the 
work  of  the  grammai-ian  and  the  {>hilologist.    We  admit  that  the 


^  Elcmcniarii  Lofiic,  p.   Kiii. 


18  FOOTNOTED  TO  FOEMAL  LOGIC 

grammatical  form  is  often  highly  ambiguous,  and  that  it  is  a  more 
or  less  successful  attempt  on  the  part  of  the  speaker  to  express 
a  meaning — it  is  a  thought  form.  But  the  thought  forms  are 
not  ambiguous,  although  they  have  manifold  meanings.  It  is 
the  work  of  the  formal  logician  to  explicate  the  various  impli- 
cations, or  manifold  meanings. 

It  is  a  significant  fact  that  in  its  indictment  of  the  Tradi- 
tional Logic  the  New  Logic  does  not  condemn  formal  reasoning 
in  toto.  Sidgwick  says:  "We  do  occasionally  reason  about  the 
extensive  relation  of  two  accepted  classes  to  each  other  by  means 
of  the  relation  of  each  of  them  to  a  third  class,  and  for  that  pur- 
pose we  may  put  letters  like  X,  Y,  and  Z,  in  place  of  the  terms 
and  so  test  the  validity  of  a  syllogism  apart  from  the  truth  of 
its  premises  and  conclusion."  (Elementary  Logic,  p.  164). 
Now  the  defenders  of  Formal  Logic  may  well  regard  this  as  a 
concession  of  the  greatest  importance.  If  there  can  be  found 
a  single  instance  where  the  form  of  thought  does  not  have  to  wait 
upon  the  matter,  controversy  is  at  an  end  and  the  formal  logicians 
have  won  the  debate.  This  is  all  that  Formal  Logic  has  ever 
contended  for,  and  we  do  not  here  avail  ourselves  of  the  prin- 
ciples that  the  exception  proves  the  rule  in  the  narrower  sense 
of  that  axiom.  These  instances,  where  it  is  admitted  that  we 
reason  formally,  are  abstractions  from  the  concrete  situations, 
and  if  the  form  can  be  divested  of  its  matter  in  a  single  instance 
there  is  nothing  to  prevent  our  applying  the  principle  univers- 
ally. 

Formal  Logic,  today,  has  set  for  itself  the  task  of  determining 
all  indefinable  concepts  and  all  indemonstrable  propositions.  The 
several  contributors  to  the  volume  on  Logic  in  the  Encyclopedia 
of  Philosophical  Sciences  are  quite  in  agreement  on  this  point. 
We  must  bear  in  mind,  however,  that  the  modern  process  of 
logical  definition  consists  in  pursuing  a  concept  back  to  some 
prior  indefinable  concept.  And  we  must  always  remark  that, 
when  we  are  dealing  with  a  class  of  inter-related  concepts,  it  is 


Till':  MODIinS  IS DICTMEST  OF  FonSIAI.  LOdlC  19 

often  immaterial  which  of  the  ^roup  are  talceii  as  the  mdehiiable 
prerequisites  of  the  others.  In  like  manner  the  present-day 
Foi-mal  Logic  regards  the  pi-oeess  of  demonstration  as  the  reduc- 
tion of  all  propositions  to  the  least  number  of  indemonstrable 
propositions.  And  here,  too,  in  considering  any  eolh'ction  of 
propositions  constituting  a  real  group  it  is  immaterial  to  the 
structure  of  the  group  which  is  placed  in  the  position  of  tlie 
indemonstrable  pi-oposition,  and  which  are  its  derivatives.'" 


IV 

Of  the  four  authors  who  in  recent  years  have  led  the  attack 
on  Formal  Logic,  Dr.  ]\Iercier  is  the  most  vehement  in  his 
denunciations  of  the  traditional  system.  He  thinks  it  a  serious 
indictment  that  among  the  foremost  writers  on  the  subject,  since 
the  time  of  Aristotle,  no  two  are  agreed  on  what  the  subject  mat- 
ter is,  what  its  limits  are,  or  even  whether  it  is  a  science  or  an 
art.  He  insists  that  it  is  neither  logical  nor  useful  to  write  upon 
a  subject  without  first  determining  the  nature  of  the  subject 
matter.  But  this  I  think  is  not  a  serious  indictment.  ]Many 
investigators  are  doing  most  logical  and  most  useful  work  in 
Dr.  Mercier's  own  special  province  of  insanity,  and  yet  we  nuiy 
say  of  these  workers,  as  Dr.  Mercier  says  of  the  formal  logicians, 
that  no  two  writers  on  the  subject  since  the  time  of  Pinel  liave 
agreed  as  to  precisely  who  should  be  included  in  the  class,  insane. 

In  his  attack  upon  the  Traditional  Logic,  Dr.  Mercier  has 
said  that  the  system  which  he  has  propounded  is  so  different 
from  all  previous  expositions  as  to  warrant  the  title,  A  New 
Logic,  which  he  has  given  to  liis  book.  I'.ut  in  the  oi)(>ning  pages 
of  the  volume  we  find  him  giving  an  account  of  the  nature  of  the 
reasoning  process  almost  identical  with  that  which  Aristotle  gave 


10  Cf.  Croce,  Encyclopedia  of  Philosophical  Sciences,  I,  186.  "It  depends 
on  us  -whether  any  particular  axiom  be  taken  as  a  theorem  and  any  par- 
ticular theorem  as  an  axiom,  according  to  the  order  which  we  adopt  in  our 
deductions. ' ' 


20  FOOTNOTED  TO  FORMAL  LOGIC 

in  the  Prior  Analytics.  Dr.  Mercier  maintains  that  there  are 
three  processes  of  reasoning — induction,  deduction  and  analogy. 
Now,  however  mucli  logicians  through  the  centuries  may  have 
differed  fi-om  Aristotle  in  their  own  personal  opinions  of  the 
nature  of  the  reasoning  process,  they  have  all  admitted  that  we 
owe  to  him  the  tripartite  division  of  the  reasoning  process  into 
analog.v,  deduction  and  induction.  Although  Dr.  Mercier  has 
condemned  in  very  emphatic  language  the  whole  of  Traditional 
Logic,  yet  when  he  comes  to  his  own  account  of  the  three  types  of 
reasoning  he  says,  when  writing  about  deduction:  "The  Logic 
expounded  in  that  book  is  the  Logic  of  Inference  ;  of  Consistency ; 
of  Proof  and  Disproof ;  of  Form.  Useless  in  the  discovery  of 
Fact ;  ignoring  the  truth  or  falsity  of  the  matter  of  which  it 
treats ;  its  value  is  in  testing  Consistenc.y ;  in  argument,  in  ex- 
plicating, convincing,  refuting.  This  is  the  field  of  Traditional 
Logic.  "^^  We  thus  observe  that  while  denying  the  uselessness  of 
the  Traditional  Logic  in  the  discovery  of  facts.  Dr.  Mercier 
nevertheless  accords  to  it  a  wide  field  of  usefulness  in  other 
directions. 

Dr.  Mercier  criticizes  the  logicians  of  the  old  school  because 
they  employ  a  nomenclature  that  is  often  inappropriate  and 
ambiguous.  He  discovers,  in  the  words  describing  the  classifica- 
tion of  propositions  as  real  and  verbal,  a  clear  misnomer  in  the 
term,  verbal;  "for  all  propositions,"  he  says,  "are  expressed  in 
words,  and  are  therefore  verbal.  Here  therefore  at  the  very 
outset  of  our  logical  studies,  we  meet  with  a  striking  instance, 
the  first  of  very  many,  of  the  inaccuracy,  looseness,  and  ambigu- 
ity with  which  words,  the  material  of  their  craft,  are  used  by 
logicians."^-  But  I  submit  that  we  should  none  of  us  write 
much  upon  the  subject  of  Logic  or  upon  any  other  subject,  if 
we  waited  until  words  said  exactly  what  they  mean,  or  meant 
exactly  what  they  said.     It  is  interesting  to  observe,  also,  that 


11  New  Logic,  p.  11. 
1-'  Op.  cit.,  p.  17. 


'/•///•;  M()i)h:i;\  isdictment  of  fol'Mal  logic  I'l 

the  classification  wliich  Ur.  Mereier  suggests,  instead  of  the 
one  ordinarily  found  in  textbooks,  is  itself  not  free  from  ambigu- 
ity of  the  very  kind  wliidi  Ik-  ci-iliciscs.  We  are  all  of  us  at  the 
mercy  of  vocabulary. 

The  idealists  join  the  empiricists  in  dtijloring  the  imperfec- 
tion of  language  as  a  means  of  conveying  thought  about  first 
principles.  It  is  not  a  new  discovery  that  language  is  inadequate 
to  speculative  thought.  Nor  does  it  rcciuire  elaborate  proof  to 
show  that  language  was  ei'eated  for  the  utilitarian  purpose  of 
comnnuiication  in  the  world  of  appearances.  The  idealist,  there- 
fore, describes  his  conceptions  of  final  reality  very  unsatisfac- 
torily bj^  means  of  a  vocabulary  which  has  had  its  origin  in  the 
world  of  relative  reality.  All  who  believe  in  the  world  of  things 
that  a])i(le,  must  therefore  express  themselves  imperfectly  by 
myth,  parable  or  metaphor.  Plato,  Christ  and  Buddha  often 
deplored  the  defects  of  language  in  their  attempt  to  teach  the 
glad  tidings  of  salvation  through  the  sense  of  the  universal.  The 
scientist  and  the  pragmatic  thinker  in  general,  who  traffic  in 
things  seen,  are  not  so  handicapped  by  the  sliort  comings  of 
language  as  are  those  who  are  concerned  with  the  unseen.  We 
make  many  allowances  for  the  scientist  when  he  expresses  him- 
self in  halting  ways  by  means  of  our  imperfect  instrument  of 
language,  which  does  not  keep  pace,  in  its  revisions,  with  the 
revisions  of  knowledge.  We  understand  the  astronomer  when 
he  says,  "Tomori'ow  when  the  sun  rises  I  sliall  make  some  obser- 
vations. ' '  We  do  not  rebuke  him  for  the  inaccuracy  and  expect 
him  to  say,  "Tomorrow  when  the  earth  revolves  and  causes  the 
sun  to  appear  to  rise,  etc."  The  idealist  bespeaks  a  like  patience 
and  tolerance  from  his  hearers  when  he  attempts  to  describe  the 
still  more  distant  realities  by  means  of  illustrations  from  the 
world  of  sense.  He  is  fully  aware  that  his  metaphors  are  faulty, 
defective,  and  inconclusive. 


FOOTNOTES  TO  FORMAL  LOGIC 


V 


The  genetic  theory  of  judgment,  upon  which  pragmatism  rests 
its  entire  logic,  is  stated  most  clearly  and  concisely  by  Mr. 
Schiller : 

I  canuot  but  conceive  the  reason  as  being,  like  the  rest  of  our  equip- 
ment, a  weapon  in  the  struggle  for  existence,  and  a  means  of  achieving 
adaptation.  It  must  follow  that  the  practical  use,  Avhich  has  developed  it, 
must  have  stamped  itself  upon  its  inmost  structure,  even  if  it  has  not 
moulded  it  out  of  prerational  instincts.  In  short,  a  reason  which  has  not 
practical  value  for  the  purposes  of  life  is  a  monstrosity,  a  morbid  aberra- 
tion or  failure  of  adaptation,  which  natural  selection  must  sooner  or  later 
wipe  awav.i3 

In  the  present  essay  I  wish  to  reaffirm  the  central  criticism 
that  idealism  has  made  upon  the  logic  of  pragmatism  ever  since 
its  birth — in  its  present  reincarnation — in  Professor  James'  lec- 
ture on  "Philosophical  Conception  and  Practical  Results,''  be- 
fore the  Philosophical  Union  of  the  University  of  California  in 
1898.  I  shall  attemi)t  to  show,  as  I  have  maintained  elsewhere^* 
that  thought  is  not  merely  an  instrument  in  the  struggle  for 
existence,  not  simply  one  of  the  devices  with  which  nature  has 
equipped  us  to  secure  a  more  comfortable  adaptation  to  our  en- 
vironment. I  shall  contend  that  aside  from  being  a  useful  instru- 
ment in  the  struggle  for  existence — its  secondary  and  derived 
function — it  has  the  more  important  primary  office  merely  to  be 
true.  It  has  been  asserted  often  in  tlu:*  history  of  Logic  that 
thought  has  an  external  meaning,  through  which  it  refers  to 
an  end  beyond  itself,  and  an  internal  meaning  which  constitutes 
an  end  in  itself.  It  is  one  function  of  judgment  to  be  useful, 
that  is,  to  reach  out  beyond  itself.  But  its  other  and  more  funda- 
mental function — a  function  without  which  that  other  function 
is  meaningless — is  just  to  be  true,  to  be  self-consistent. 

Some  pragmatists  have  hestitated  to  conunit  themselves  to  the 
doctrine  that  all  judgments  are  practical.     Such  leaders,  \\o\\- 


'^?' Humanism:  PItilosoplucal  essays  (London,  Macmillan,  1903),  p.  7. 

14  " Pragmatism  and  the  a  priori,"  Present  series,  I  (1904),  pp.  72-91. 


'/■///■;  MiiDEUS  I \ nil  I  M EST  OF  FOUM.tt.  LOC.IC  23 

ever,  as  Schillcf,  Sicl<i\\  ick  and  Mcrcici'  have  iiulicsitatingly 
declared,  not  only,  that  all  ttiifli  works,  hut  also  that  all  that 
works  is  true  I  Jut  I'ToTcssor  Dewey  scfuis  always  to  leave  liis 
i-eaders  in  douht  as  to  preeiscly  what  view  he  holds,  in  liis  very 
latest  utteranees  he  has  again  failed  to  nuike  his  position  clear. 

In  an  artiele  entitled,  "An  Alleged  New  Discovery  in  Logic" 
Ml-.  1).  S.  Robinson  criticises  Professor  Dewey's  Experimental 
Jjogic  and  reniai'ks'''  that  he  is  in  doubt  whether  Professor  Dewey 
would  say  that  all  judgments  are  ])raetieal.  In  his  rejoinder 
Professor  Dewey  admits  "Tliere  is  dangei-  of  a  s<'i'ious  ambiguity 
in  discussing  practical  judgments  as  a  distinctive  type  and  also 
intimating  that  in  some  sense  all  judgments  may  be  practical." 
I>ut  when  Professor  Dewey  "intimates"  (not  asserts),  that 
"some"  (not  all)  judgments  "may  be"  (not  are)  practical,  I, 
too,  find  myself  in  dou])t.  1  am  still  old-fashioned  enougli  in  my 
idealistic  convictions  to  think  that  the  praguuitist  can  not  avoid 
committing  himself  to  at  least  one  assertion  that  is  not  prac- 
tical— or  at  any  rate  not  practical  in  the  same  sense  as  the 
others —  namely,  this  very  judgment  that  all  judgments  are  i)rac- 
tical.  And  it  is  not  mere  (juibbling  to  say  that  the  judgment 
that  all  judgments  are  practical,  is  not  itself  a  practical  judg- 
nu'nt.  It  is  another  way  of  saying  that  the  judgments  of  utility 
are  in  one  dimension  of  thought  and  the  judgments  that  pro- 
nounce upon  the  members  of  the  series  of  useful  judgments  are 
in  a  different  dimension  of  thought. 

Empirical  Logic^"  has  always  declared  that  all  definition 
presupposes   a    psychological   treatnu^nt    of   nunital    states;    and 


1^' Jour,  philos.  and  i)syt'li.,  XLV,  225,  April  26,  1917. 

i«  There  is  an  important  sense  in  which  every  theory  of  judgment  is 
empirical.  When  I  say  that  a  judgment,  or  anything  else,  is  empirical, 
one  implication  always  is  that  it  might  have  been  othiM-wiso.  And  in  our 
theory  that  judgment  is  just  such  a  selection  from  competing  alternatives 
presented  to  the  mind,  this  constitutes  one  of  the  earliest  and  most  basic 
characteristics  of  the  judging  consciousness.  Wherever  Ave  find  the  possi- 
bility of  error,  we  are  dealing  with  empirical  facts.  And  there  is  this 
paradox  about  facts:  to  be  real  facts  they  must  possess  the  inherent  possi- 
bilitv  of  being  different,  and   hence  not  facts. 


24  FOOTNOTES  TO  FOEMAL  LOGIC 

idealists  have  always  admitted  that  a  study  of  psychic  facts  as 
they  are  immediately  presented  to  consciousness  is  indispensable 
to  any  doctrine  of  truth.  But  they  .insist  that  this  is  not  the 
sufficient  condition  of  truth;  the  apperceiving  or  unifying  of 
the  sense-presented  facts  is  performed  by  the  self-active  prin- 
ciple of  mind.  If  there  is  value  to  our  individual  experiences,  as 
they  come  to  us  strung  along  in  time,  and  if  it  is  unnecessary 
to  make  this  temporal  validity  rest  back  upon  a  validity  that  is 
not  in  time,  all  talk  about  a  world  of  absolute  truth  and  perfec- 
tion is  meaningless.  If  Experimental  Logic  is  self-sufficing,  then 
there  is  no  Logic  uljeHiaupt. 

Experimental  Logic  would  explain  my  present  thought  by 
locating  it  between  an  a  priori  situation  out  of  which  it  emerged 
and  a  subsequent  situation  into  which  it  flows.  Idealistic  Logic 
maintains  that  the  three  situations — past,  present  and  future — 
even  when  thus  casually  connected  in  the  chronological  series 
are  not  self-explanatory.  There  is  exhibited  in  Instrumental 
Logic,  we  hold,  the  ancient  fallacy  of  failure  to  distinguish 
between  psychological  cause  and  logical  ground. 

The  logical  coherence  in  our  judgments,  according  to  Experi- 
mental Logic,  is  our  interest  in  the  situation  in  which  we  find 
ourselves,  when  called  upon  to  judge.  We  are  constrained  to 
reconstruct  that  part  of  the  world  with  which  we  are  in  imme- 
diate contact.  The  union  of  the  subject  and  predicate  in  judg- 
ment is  the  outer  expression  of  this  purpose  or  interest.  This  is 
certainly  true  as  a  psychological  account  of  the  judging  process. 
But  having  said  that  interest  or  purpose  is  the  cause  of  the  inter- 
connection of  ideas,  we  still  have  on  our  hands  the  more  serious 
problem  of  finding  the  ground  of  the  present  purpose.  This, 
as  the  idealist  has  often  insisted,  is  not  self-explanatory  for  cause 
and  ground  are  not  identical.  It  is  one  thing  to  say  that  we 
judge  because  we  have  a  need,  an  interest,  or  a  purpose ;  but  an 
entirely  diiferent  thing  to  discover  the  ground  of  this  need.  How 
may  I  know  that  this  present  purpose  to  reconstruct  reality  is  a 


7  ///•;  M()i)i:i:s  isdictment  of  formal  logic  25 

true  purpose?  Only  when  I  have  laid  hold  of  a  higher  and  ulti- 
mate puri)Ose,  namely,  a  criterion  of  this  speeific  purpose.  In 
short,  I  fail  to  see  liow  i)ui"poses  are  capable  of  self-evaluation. 

Experimental  Logic  while  emphasizing  effects  of  action  as 
tests  of  validity,  does  not  furnish  a  criterion  by  means  of  which 
we  may  distinguish  good  from  bad  effects.  Every  judgment 
reconstructs  reality,  and  thereby  helps  to  continue  the  present 
order,  say  the  defenders  of  the  new  theory  of  knowledge.  We 
pronounce  the  judgment  true  if  it  contributes  to  the  existing 
order,  and  false  if  it  does  not.  But  now,  in  order  that  we  may 
distinguish  a  good  effect  fi-om  a  bad  one,  we  need  some  criterion 
extrinsic  to  the  situation  to  tell  us  whj''  it  is  best  to  have  the 
present  system  i)erpetuat('d.  In  every  experimental  logic,  truth 
means  objcetiviTy.  and  its  criterion  is  utility.  But  in  the  prac- 
tical world  there  are  different  kinds  of  utility.  If  the  useful  is 
the  true,  we  ought  likewise  to  have  grades  of  truth,  and  be  able 
to  speak  of  the  true,  the  truer  and  the  truest.  This  is,  indeed, 
precisely  wliat  the  pragmatist  does  say — a  doctrine  open  to 
criticism,  to  say  the  least.  iNEoreover,  even  if  we  admitted  the 
possibility  of  gradations  in  truth  (for  the  logic  of  realism  insists 
that  this  is  by  no  means  manifestly  absurd),  the  pragmatic  test 
furnishes  no  criterion  for  distinguishing  between  the  different 
kinds  of  truth.  But  it  is  evident  that  it  is  not  mere  utility,  but 
utility  of  the  right  kind,  that  is  needed  to  establish  the  objectivity 
in  judgment.^' 

In  every  judgment,  according  to  the  pragmatic  theory  of 
knowledge,  something  new  is  added  to  the  system  of  cognitions 
already  in  the  possession  of  the  one  who  judges.     The  test  of 


1' Cf.  "Windelbaml,  Ency.  FliHo.s.  ScL,  I,  24.  "And  here  we  t-ome 
on  a  double  aspect  of  all  logical  laws:  on  the  one  hand  they  are  rules  for 
the  empirical  consciousness,  according  to  which  all  thinking  which  has  truth 
for  its  aim  should  be  carried  on ;  on  the  other  they  have  their  inner  and 
independent  significance  and  being,  quite  independent  of  the  actual  hap- 
pening of  ideational  processes,  which  are  or  are  not  in  accordance  with 
them.  We  may  call  the  latter  their  value-in-themselves,  the  former  their 
ralue-for-u.'i. ' ' 


26  FOOTNOTES  TO  FOBMAL  LOGIC 

the  rationality  of  this  new  element  is  its  compatibility  witli  the 
old.  If  it  works  it  is  pronounced  true,  and  is  given  its  api)ropriate 
place  in  the  established  order.  If  it  does  not  tit  in  with  the  old 
it  is  rejected  as  false.  But  this  definition  of  truth  is  more  adroit 
than  accurate.  Is  not  the  pragmatist  all  the  while  begging  the 
whole  question  ?  Does  he  not  presuppose  the  truth  or  rationality 
of  the  old,  namely,  this  thought  system  wliich  he  possesses  at 
the  moment  of  judgment?  His  criterion  of  inner  consistency 
w^orks  very  well,  if  we  grant  him  enough  rationality  to  start  the 
process.  The  instrumentalist,  I  should  say.  borrows  just  enough 
of  the  idealistic  insight  to  set  his  scheme  in  motion  and  then  dis- 
avows the  debt.  The  idealist  has  ever  insisted  that  this  determin- 
ation of  the  primal  rationality  can  never  be  achieved  by  a  jjoste- 
riori  methods.  That  which  is  workable  is  not,  for  that  reason 
alone,  true.  A  new  fact  may  fit  in  with  the  old,  and  yet  may 
not  know  itself  to  be  error,  because  it  does  not  know  tlie  system 
into  which  it  has  been  accepted,  is  false. 

I  cannot  think  that  the  total  meaning  of  an  idea  is  to  be 
found  by  searching  only  forward  from  the  idea  to  its  conse- 
quences, as  Professor  James  teaches,  nor  yet  by  looking  both 
forward  and  back  as  Professor  Dewey  and  his  disciples  insist. 
The  deepest  truth  about  thought  is  found  in  an  entirely  different 
dimension.  It  lies  in  a  world  that  is  logically  prior  to  the  postu- 
lates of  either  of  these  forms  of  pragmatism.  Thought  is  con- 
structive as  well  as  reconstructive.  It  is  not  merely  an  instru- 
ment in  the  struggle  for  existence,  but  is  itself  legislatively 
sovereign  over  the  process  of  evolution  within  which  it  manifests 
itself  as  an  instrument.  Not  what  an  idea  has  come  out  of,  nor 
what  it  is  just  now  seen  to  be,  nor  what  it  is  going  to  do  here- 
after, but  what  it  eternally  is,  must  furnish  us  with  our  d(^epest 
insight  into  the  nature  of  thought. 


THK  MODKUS  ISDK'TMKST  OF  FOUMM.  LOCK'  27 


VI 

The  agnostic  rcalisiii  n\  llic  heart  of  vm-vx  U)v\\\  of  pragmatic 
logic  is  not  easy  to  refute.  It  has  dcsceiuh'd  directly  from  the 
agnosticism  of  the  Criliqin  of  Pure  Reason.  The  only  way  to 
dissolve  this  realism  is  to  make  use  of  Kant's  own  discovei-y,  and 
pursue  his  logic  to  tiie  legitimate  conclusion  of  its  own  movement. 
Kant  pointed  out  the  path  that  must  be  pursued  in  order  to 
explain  the  inherent  contradictions  in  the  realistic  conception 
of  causality.  He  demonstrated,  it  would  seem  foi'  all  time,  that 
the  principle  of  efificient  catujality  cannot  belong  to  reality.  l)ut 
that  it  is  the  mind's  contribution  to  experience.  However,  he 
failed  to  see  that  for  this  very  reason  there  can  be  no  genuine 
datum  in  knowledge.  If  the  facts  of  experience  are  really  given, 
if  they  are  thrown  at  the  mind  from  the  world  of  things  in 
themselves^then  this  transcendent  reality  possesses  the  i)rinci- 
ple  of  efificient  causality.  This,  however,  Kant's  own  doctrine 
explicitl}'  denies.  His  insight  enables  us  to  see  what  he  him- 
self seems  never  to  have  been  fully  aware  of,  that  if  the  things- 
in-themselves  have  not  in  them  the  principle  of  efificient  causality 
they  are  incapable  of  giving  anything  to  mind.  Things-in-them- 
selves  can  not  contribute  causally  to  the  content  of  knowledge. 

The  fundamental  point  at  issue  between  Plato  and  Aristotle 
on  the  import  of  judgment  has  been  perpetuated,  in  philosophical 
discussions,  to  the  present  day.  The  idealists  say  with  Plato 
that  necessary  truth  is  that  from  whicli  every  purely  material 
external  or  given  element  has  been  cancelled.  The  only  truth  is 
formal  truth.  The  later-day  pragmatic  or  instrumental  logicians 
have  insisted  that  trulh  as  thus  defined  would  he  relegated  to 
the  world  of  matliematical  abstraction,  to  the  realm  of  "bloodless 
categories."  Plato  ])rovided  for  a  more  vital  connection  between 
the  universal  and  the  particular,  the  abstract  and  the  concrete 
than  appears  on  the  surface.  Ai-istotle's  attack  on  Plato  on 
this  subject  was  not  entirely  defensible.    And  no  serious  idealism 


28  FOOTNOTES  TO  FOEMAL  LOGIC 

at  the  present  time  imposes  this  requirement  on  knowledge.  Plato 
did  not  demand  that  the  given,  the  concrete,  the  particular  ele- 
ment in  knowledge  should  vanish  entirely.  Now  it  is  obviously 
a  question  as  to  the  precise  meaning  of  the  given.  The  given 
may  be  so  defined  that  it  can  be  kept  as  a  constituent  element  of 
the  highest  knowledge.  A  datum  which  is  just  hurled  at  a  passive 
mind  would,  of  course,  contaminate  knowledge  and  forever  reduce 
it  to  relativity  and  incertitude.  In  perfect  knowledge  there  can 
be  no  Streng-gegchenes,  nothing  genuinely  novel  or  totally  differ- 
ent. But  the  logic  of  naive  realism  declares  that  such  a  Streng- 
gegehenes  is  an  inexplicable  and  irreducible  element  of  the  know- 
ing process.  Absolute  knowledge,  it  declares,  is  forever  impos- 
sible; such  opinions  or  beliefs  as  we  have,  we  arrive  at  by  a 
posteriori  methods  entirely.  The  logic  of  nai've  realism  and  the 
Instrumental  Logic  declare  that  we  are  not  at  all  concerned  with 
the  ultimate  beginning  of  thought.  In  fact,  thought  cannot  be 
traced  back  to  its  source.  It  cannot  see  itself  start;  it  must 
simply  accept  itself  as  fact.  But  now  it  can  be  pointed  out,  even 
to  the  proverbial  /ji^awi  man  on  the  street,  that  there  can  be  no 
arriving  at  knowledge  or  anything  else  without  starting.  There 
must  be  a  beginning  somewhere,  an  initial  point  of  departure 
which  is  itself  underived. 

VII 

Empirical  Logic  has  always  dealt  extensively  with  the  word 
fact.  All  knowledge,  it  says,  must  have  its  foundation  deep  down 
in  the  world  of  concrete  fact.  To  this  we  may  reply :  In  order 
to  realize  itself,  thought  must,  to  be  sure,  pass  through  fact. 
This  Plato  never  denied,  and  the  student  in  the  philosophy  of 
Kant  learns,  almost  in  his  first  lesson  that  the  a  priori  forms  of 
thought  are  empty  and  without  meaning,  until  they  have  received 
their  material  filling.  Thought  does  not  see  itself  start.  But  we 
are  not  warranted  in  saying  that  because  it  does  not  see  itself 
start,  it  arrives  without  starting.    Of  course,  men  reasoned  acccii- 


TIIF.  M()I>I:U\  IMJICTMENT  OF  F(U:MAL  fJJGIC  29 

rately  before  they  knew  the  reason  for  their  accurate  reasoning. 
They  followed  out  premises  to  their  conclusion,  or  traced  con- 
clusions hack  to  their  gr'ouiiils,  j^Miidcd  by  i)rinciples  of  correct 
tliiukiii^-  hffoi'c  tliose  i)rinciples  were  noticed  or  understood. 
Aristotle  was  preceded  by  many  centuries  of  exact  thinking.  It 
was  not  his  primary  purpose  to  make  men  rational — that,  for 
the  most  part,  they  already  were.  He  was  interested  to  show 
men,  by  critical  analysis,  in  what  their  existing  rationality  con- 
sisted. 

Thouglit  does  first  Ix'conie  aware  of  its  own  movement  as  it 
passes  through  fact — as  it  issues  out  of  one  situation  to  go  over 
into  another.  But  this  is  not  the  last  step  in  its  self-realization. 
It  is  an  unjustified  arrest  of  thought's  activity  not  to  allow  it 
to  jiass  through  fact  and,  returning  to  itself,  to  discover  the 
lotderivcd  laws  of  its  movement.  Thought  does  find  itself  by  the 
way  of  fact,  but  when  its  activity  is  unhindered  it  passes  to  the 
higher  level  where  it  sees  that  itself  furnishes  the  prior  condition 
of  the  discovery  of  itself  in  the  facts.  To  think  actually,  we  must 
indeed  think  about  something;  this  something,  the  object  matter 
of  thought,  what(>ver  it  may  be,  must  in  the  first  instance  be  sup- 
plied through  the  medium  of  the  senses.  Thought  itself  does  not 
become  an  object  of  thought  until  after,  it  has  been  called  into 
exercise  by  objects  presented  from  without.  But  while  the  mate- 
rial or  external  element  varies  with  every  successive  act  of 
thought,  the  formal  or  internal  element  remains  the  same  in  all ; 
thus  the  necessary  law,  or  form,  binding  on  the  thinker  in  every 
instance,  is  distinguished  from  the  contingent  objects,  about 
which  he  thinks  on  this  or  that  occasion.  Obviously  the  words 
material,  external,  and  <)])ji('t  are  not  here  employed  in  any  naive 
sense.  In  a  later  chapter,  when  we  come  to  discuss  more  in 
detail  the  nature  of  the  objective  element  in  thought  we  shall 
define  the  object  entirely  in  terms  of  the  expected  self -trans- 
cendence of  the  subject. 

The   now   pragmatic   Logic   and   the   mod(M-n   r(\ilistie   meta- 


30  FOOTNOTES  TO  FOBMAL  LOGIC 

physics  underlying  it  —  so  their  devotees  frankly  confess  — 
acknowledge  important  contributions  which  they  claim  modern 
natural  science  makes  to  their  doctrine.  There  has  been  a  very 
prevalent  tendency  in  the  thinking  of  the  last  quarter  of  a  cen- 
tury, to  abandon  or  to  ignore  almost  entirely  what  through  all 
the  ages  has  been  considered  the  highest  concern  of  the  human 
mind,  namely,  the  search  for  first  principles,  logically  prior  to  the 
causal  series  and  its  validating  ground  in  time  and  space.  This 
tendency  to  abandon  all  attempts  to  orient  our  temporal  experi- 
ences— our  djmamic  lives- — ^by  resting  them  back  upon  a  static 
encircling  reality  is  undoubtedly  due  to  the  enormous  place  that 
the  method  of  natural  science  has  come  to  occupy  in  the  higher 
intellectual  life  of  our  time.  The  vast  and  comparatively  sudden 
development  in  the  biological  sciences  under  the  guidance  of  the 
master  principle  of  evolution  has  filled  many  minds  with  an  over- 
powering sense  of  the  importance,  the  certainty  and  the  useful- 
ness of  this  principle  in  other  fields.  But  there  are  yet  many 
unshaken  idealists, ^^  who  still  believe  that  Kant's  first  question, 
' '  What  can  I  know  and  how  do  I  know  it ! "  has  to  be  raised  and 
answered,  too,  in  a  final  and  affirmative  fashion,  before  the 
scientist  has  valid  possession  of  his  method  even  within  the  field 
where  alone  it  is  applicable.  The  validity  of  the  scientific  method, 
lies  entirely  in  its  application  to  its  proper  object,  namely,  the 
facts  of  sensible  experience  both  inner  and  outer.  But  it  does 
not  follow  that,  because  science  can  give  no  certitude  in  the  real 
world  beyond  sense,  there  is  no  method  of  certainty  possible  in 
that  super-sensible  world.  Metaphysics  is  absolutely  indispens- 
able to  the  existence  of  Logic  or  of  any  other  science. 

The  theory  of  judgment  that  is  offered  in  these  pages  demands 
an  objective  system  which  the  judgment  itself  confesses  must  lie 
beyond  its  primary  activity.     But  this  postulated  objectivity  in 


]«E.g.,  Windelband  says:  "Modern  Metaphvsie,  with  its  attempts  to 
piece  itself  together  out  of  t)orrowings  from  the  sciences,  is  far  more  con- 
temptible than  the  old  Ontology  which,  starting  from  the  realm  of  validity, 
had  at  any  rate  the  courage  to  attempt  the  deduction  of  the  interconnection 
of  the  universe  as  an  articulated  whole. ' '    Ency.  Philos.  Sci.,  I,  65. 


•/•///•;  MODF.US  l\l)l<  TMhXT  OF  FOUMAI.  LOCK'  .'A 

judf^iiiciit,  as  T  sliall  t  I'v  to  sli()\\-  latcc,  is  not  iiieonsistciit  with  a 
monistic  theory  of  \\\r  iiiii\<'i'sc  :  il  is  even  coiiipatibh'  witli  the 
most  naive  siihjeclixc  idealism.  How cNcr,  it  pfovides  for  a  relax- 
ing of  a  too-rif^fid  monistic  ontology.  Wlien  we  declare  that  the 
subject  awaits  its  object,  and  then  define  tiiat  object  as  no  other 
than  this  expected  self-ti'anscendinp,  synthetic  achievement  of 
the  sul)ject,  we  avoid  tiie  coiit  radiet ions  of  an  epistemological 
dualism  on  the  one  hand,  and  an  ontoloj^ical  monism  on  the  other. 
Hoth  for  knowledge  and  for  existence  the  idea  and  its  object 
are — to  use  Bradley's  very  apt  expression — "coupled  apart." 

The  New  Logic  is  distinguished  fiom  all  the  oldei-  idealistic 
systems  by  its  refusal  to  accept  the  distinction  between  fjround 
hi  fact  and  ground  in  thought.  As  has  now  frequently  been 
pointed  out,  pragnuitic  Logic  dispenses  entirely  with  ontology  in 
the  historic  sense  of  the  word,  and  therefore,  identifies  the  cause 
of  the  existence  of  serial  facts —  in  their  serial  manifestation — 
and  the  ground  of  our  thinking  them  serially.  We  hold  that  this 
distinction  is  vital  and  that,  wlnle  there  is  a  i)ractical  viewpoint 
from  which  it  may  be  ignored,  it  cannot  be  totally  cancelled.  This 
is  one  of  the  first  and  most  persistent  criticisms  that  various 
idealists  have  made  upon  the  instrumental  theory  of  judgment. 

The  genetic  tlieories  of  judgment  are  all  comjjelled  to  admit 
that  the  ground  of  belief  is  finally  an  unsolved  problem.  Psy- 
chology seems  to  have  discovered  that  chronologically  we  believe 
things  first  and  afterwards  demonstrate  tliem.  Thinking  as  dis- 
tinguished from  believing  is  retrospective  rathei-  than  prospec- 
tive ;  it  is  demonstration  rather  than  inference.  Now  it  is  not 
only  Psychology  that  confesses  itself  baffled  with  this  puzzling 
question  of  the  reason  foi-  our  beliefs,  but  Logic  also  finds  the 
ground  of  knowledge  in  a  sense  inexplicable.  As  I  have  already 
said,  knowledge  is  a  postulate  of  logic;  it  is  a  fact  that  must  be 
assumed  before  logic  itself  can  come  into  existence.  If  Logic 
is  "tldnking  about  thought,""  tlieii  this  tliouglit  is  ol)vi()usly  taken 
for  granted  when  tjie  tliiid<ing  about  it  begins. 


32  FOOTNOTES  TO  FORMAL  LOGIC 

Professor  Dewey  has  often  admitted/^  by  implication  at  any 
rate,  that  he  has  not  remained  true  to  the  Hegelian  idealism  of 
his  earlier  writings.  And  yet  many  of  his  later  utterances  seem 
to  me  as  entirely  opposed  to  the  naive  associationism  of  the  earlier 
empiricists,  Locke,  Mill,  and  Bain,  as  is  any  idealism.  And  there 
are  also  serious  divergencies  from  the  even  more  radical  empi- 
ricism of  the  later  pragmatists,  Schiller,  Sedgwick  and  Mercier. 
For  Professor  Dewey's  ideas  taken  by  themselves  are  entirely  dis- 
crete facts.  They  are  continuous  only  when  embedded  in  the 
specific  situation  out  of  which  they  arise  and  into  which  they 
descend.  And  yet  I  must  repeat  that  I  fail  to  see  how  the  "situa- 
tion" with  all  its  "brute"  objectivity  can  ever  provide  for  the 
continuity  that  is  necessary  for  "knowing  things  together." 

I  wish  to  offer  a  homely  illustration  of  an  illusion  of  continuity 
in  the  optical  world  analogous  to  the  essential  discontinuity  that 
lurks  in  the  instrumental  theory  of  thought.  Each  of  the  various 
moments  of  a  motion  picture  as  they  are  flashed  on  the  screen 
might  be  described  in  terms  of  what  precedes  and  what  follows 
it.  "We  say  we  watch  the  scene  being  enacted,  we  follow  the  plot 
and  we  think  we  see  explanatory  continuity  there.  But  if  an 
imaginary  being,  living  in  that  screen  world — totally  unaware  of 
the  projecting  power  of  the  stereopticon — were  asked  to  give  an 
account  of  what  really  does  happen,  he  would  say  precisely  what 
Hume  said  about  the  world  that  we  actually  see.  No  causal  con- 
tinuity is  found  on  the  screen.  One  picture  appears  and  then 
disappears  and  another  totally  disconnected  from  the  preceding 
one  takes  its  place.  The  clever  makers  of  the  motion  pictures, 
taking  advantage  of  actual  discontinuity,  can  feign  all  kinds  of 
continuity  by  piecing  together  parts  of  films  taken  miles  and 
days  apart.    The  only  truly  explanatory  continuity  is  found  when 


19  Cf .  Studies  in  Logical  Theory,  p.  36.  ' '  There  is  no  such  thing  as  either 
coincidence  or  coherence  in  terms  of  the  elements  or  meanings  contained  in 
any  couple  or  pair  of  ideas  taken  by  itself.  It  is  only  when  they  are  co-factors 
in  a  situation  or  function  which  includes  more  than  either  the  "coincident" 
or  the  "coherent"  and  more  than  the  arithmetical  sum  of  the  two,  that 
thought 's  activity  can  be  evoked. ' ' 


THE  MODEKS  IXDICTMKXT  OF  F()i:MAL  LOGIC  33 

we  read  our  way  back  at  each  instant  to  and  through  the  project- 
ing power  of  the  stereopticon  itself.  So,  too,  must  the  states  of 
consciousness  tliat  api)ear  (■lir()ii()h)^'ically  in  thi-  instrumental 
theory  of  judgment  be  translated  into  a  thouglit  process  tliat 
transcends  time  and  of  which  tliat  outer  evolution  is  but  the 
projection. 

A  less  concrete,  and  therefore  in  some  ways  a  moi'e  satisfac- 
tory illustration  ma}'  be  taken  from  geometry  to  show  the  essen- 
tial discontinuity  in  the  stream  of  consciousness.  The  points  of 
a  parabola,  for  example,  take  their  places  seriatim  in  obedience 
to  the  requirements  of  facts  external  to  themselves.  Each  point 
obeys  the  law  of  keeping  e(|uidistant  from  a  fixed  straight  line 
and  a  fixed  point;  as  a  particular  fact  in  the  series,  it  is  inde- 
pendent of  the  points  that  lie  next  to  it.  An  external  spectator 
might  imagine  that  the  points  arranged  themselves  in  this  orderly 
fashion  by  a  kind  of  reciprocal  reference  to  each  other.  Each 
point,  it  might  be  thought,  could  find  its  place  in  the  series  by 
taking  its  bearings  from  its  predecessor  and  passing  the  angular 
reading  on  to  its  successor.  But  the  curve  has  no  such  intrinsic 
principle  for  its  spatial  determination ;  it  is  the  result  of  the  indi- 
vidual compliance  of  each  point  with  entirely  external  conditions. 
The  straight  line,  however,  can  and  does  define  itself  as  a  quantity 
in  extension  by  precisely  such  an  intrinsic  principle.  One  has  a 
practical  illustration  of  this  in  watching  a  company  of  soldiers 
"fall  into  line." 


CHAPTER   II 

APPEEHENSION.  QUESTION  AND  ASSERTION 

I 

It  has  frequently  been  maintained  that  Logic  is  not  concerned 
with  the  question  as  to  the  structure  of  the  idea,  or  how  many 
ideas  may  be  grasped  in  a  single  pulsation  of  consciousness,  or 
any  other  of  the  many  questions  in  which  one  idea  is  involved. 
The  unit  of  Logic,  we  are  told,  is  the  judgment,  and  every  judg- 
ment contains  at  least  two  ideas.  Bradley  and  his  disciples  have 
rightly  rejected  the  view  that  judgment  is  the  comparison  of  two 
ideas.  However,  there  is  a  sense  in  which  Ave  may  say  that  iwo 
idea's  are  involved  in  every  judgment.  Tlie  ultimate  molecule  of 
knowledge,  to  use  a  chemical  metaphor,  is  always  diatomic.  Con- 
scious judgment  is  the  idea  that  I  have  an  idea.  To  have,  or  to 
entertain  an  idea  is  to  refer  it  to  reality ;  but  this  reference  of  the 
idea  to  reality  implies  at  least  one  other  idea  which  might  have 
been  referred  to  reality  instead.  If  we  had  only  one  idea  we 
should  never,  I  think,  distinguish  between  it  and  reality  and  we 
should  never  talk  of  referring  it  to  reality. 

Obviously,  these  questions  which  lie  in  the  borderland  of 
controversy  between  Logic  and  Psychology  can  never  be  settled 
until  we  know  precisely  what  we  are  to  understand  by  one  idea. 
If  we  mean  by  an  idea  a  state  of  consciousness  so  immediate  and 
withal  so  simple  and  single  in  its  structure  as  to  exclude  all 
internal  multiplicity,  then  Logic  can  have  nothing  to  do  with 
it,  and  perhaps  not  Psychology,  since  the  existence  of  a  mental 
state  described  by  Jevons  and  the  earlier  logicians  and  psycholo- 
gists as  simple  apprehension,  has  justly  been  called  in  question. 
That  may  always  be  regarded  as  one  idea  which  includes  within 

[34  J 


.\i'i'i:i:ii i:S sios.  (jri-:sri().\  axd  .isshiniox  35 

its  syntlu'tic  ^ra.sp  jill  llic  .sct'Oiidai'V  ideas  wliicli  a  purposive  will 
cares  to  make  in  it.  It  is  the  pui-pose  1o  hold  the  multiplicity  as 
a  single  object  of  attention  that  makes  it  one  idea.  Tin-  oid\'  ti"ue 
individual  is  a  will-object,  l-'iom  the  point  of  view  of  the  act  of 
synthetic  attention  the  idea  is  one,  but  it  is  not  on  that  account 
sim])le.  Foi'  this  icasoti  the  exj)ression  simple  a{>prehension  is 
a  misnomer.  Apprehension  nuiy  be  of  multiple  content.  For  the 
pui'i)0se  of  the  present  discussion  we  need  not  go  furthei-  into  thi.s 
controversy. 

It  should  be  pointed  out.  however,  that  the  expressions,  mental 
states,  state  of  consciousness,  idea,  image,  are  all  of  them  ambig- 
uous, and  this  ambiguity  wlien  carried  ovei-  into  tlie  logical  debat(^ 
becomes  the  source  of  hopeless  confusion,  and  the  "cause  of  all 
our  woes."  No  woi-d  in  Logic  has  caused  more  confusion  than  the 
word  idfci.  Even  in  ordinary  usage  it  has  been  taken  to  stand 
for  both  a  universal  and  a  particular  content  of  consf(*ionsnp.«4.<;  It 
would  be  better  to  regard  the  idea  as  one  aspect  of  the  concept. 
My  concept  of  a  tree  may  be  analyzed  into  tiii-ee  moments:  (1) 
the  existence  of  an  image  in  the  mind  which  might  be  called  my 
idea  of  the  tree,  (2)  the  aggregate  of  inner  (|ualities,  (3)  the  ex- 
ternal reference  or  significance.  Bradley,  as  is  well  known  has 
characterized  these  three  moments  as  (1)  the  flial,  (2)  the  ichdl. 
and  (3)  the  meaning  of  the  idea.  Logicians  and  psychologists  still 
use  the  word  idea  instead  of  concept,  wliicli  is  freer  from  ambig- 
uity. The  concept  is  not  exhaustively  understood  when  it  is 
treated  psychologieall}'  only  ;  it  is  more  than  just  a  simple  psychic 
act.  The  word  idea  in  its  more  limited  u.se  does  stand  for  such  a 
focus  of  analytic  attention.  Rut  no  idea  is  mere  idea  ;  tlie  cogni- 
tive function,  that  is.  the  i-elation  to  something  beyond  itself. 
which  it  means,  is  necessary  to  the  very  being  of  the  idea.  And 
yet,  self-contradictory  as  it  may  appear,  we  must  say  that  when 
we  have  an  idea  of  an  object  that  object  is  already  an  essential 
l^art  of  the  idea.  Vov  Logic,  the  idea,  or  mental  state  is  a  on< 
enwrapjung  a  nnmii.     It  is  a  content  contemiilated  from  a  nuil- 


36  FOOT  NOT  EH  TO  FOBMAL  LOGIC 

tiple,  that  is,  a  dual  viewpoint.  From  one  of  these  points  of  view 
the  idea  or  concept  is  a  plurality ;  in  its  outward  relation  to  the 
rest  of  the  universe  it  is  many.  But  when  it  faces  the  thinker,  it 
is  one ;  its  former  plurality  has  now  become  the  object  of  a  single 
act  of  attention. 

Some  psychologists  have  analyzed  thought  out  into  a  serial 
arrangement  of  its  acts  in  which  we  find  the  concept  placed 
between  the  judgment  and  abstraction.  The  judgment  depends 
upon  the  concept  and  the  concept  in  turn  depends  upon  the  pro- 
cess of  abstraction.  No  serious  objection  can  be  made  to  this 
serial  arrangement  if  we  do  not  construe  the  relationship  of 
dependence  as  a  uni-directional  function.  The  structure  of  the 
concept  and  the  judgment  are  different  only  for  Psychology,  for 
Logic  they  are  identical.  When  I  say  the  shy  is  Mue  there  is  pre- 
cisely the  same  thought  of  the  relation  in  the  act  involved  as  when 
I  say  the  Mue  sky.  The  difference  lies  in  the  fact  that  the  concept 
is  pure  receptivity  while  the  judgment  meets  the  datum  with  a 
reaction  in  the  form  of  an  acceptance  or  a  rejection.^  The  judg- 
ment discovers  the  concept  as  an  isolated  state  of  consciousness, 
atrophied  or  bereft  of  the  support  of  reason.  It  rehabilitates  it 
by  connecting  it  again  with  its  reasons.  There  is,  therefore, 
partial  justification  for  regarding  the  concept  as  prior  to  the 
judgment.  But  on  the  other  hand  the  concept  in  the  first  instance 
was  constituted  by  an  act  of  judgment  or  abstraction,  and  so 
there  is  truth  in  the  remark  that  judgment  both  precedes  and 
follows  the  concept.  Again  we  must  observe  here  the  distinction 
between  idea  and  concept.  The  idea  is  always  particular ;  it  is 
composed  of  sensuous  elements  and  is  static.    The  concept  is  uni- 


1  Croee  seems  to  discredit  unduly  such  an  analysis  of  the  content  of 
consciousness.  He  remarks :  ' '  This  division  concept,  judgment  and  con- 
clusion involves  the  assumption  that  three  different  moments  can  be  dis- 
tinguished within  what  is  really  a  single  and  unanalysable  act  of  thought. 
As  a  matter  of  fact,  no  one  will  ever  succeed  in  thinking  a  concept,  a  real 
concept  or  a  judgment  which  is  not  at  the  same  time  a  conclusion,  being 
connected  in  a  system  with  other  conceptions  and  judgments. "  It  is 
doubtless  true  as  Croce  says  that  no  one  will  ever  think  a  concept  by  itself, 
but  it  is  not  impossible  to  think  the  concept  in  its  coordinated  position 
within  the  whole  of  a  specific  content.     Encj).  Fliilos.  Sci.,  I,  202. 


.\rri:i:ii i:\  sios,  (ji  jisriox  .i\i>  .issi'imo.x  ;j7 

vcrsal ;  it  is  the  jjow  er  or  capacity  of  a  pcrcci^tion  to  mean  some- 
thing— to  stand  for  something  external  to  itself.  The  idea  is  the 
psychical  image  that  comes  and  goes.  The  concept  is  the  signi- 
fication  or  the  fixed  content. 

13erkeley  and  the  otiier  nominali.sls  wcie  ]>lainly  rij^dit  in  their 
criticism  of  Locke's  doctrine  of  abstract  ideas.  Locke  described 
the  process  of  abstraction  as  an  affirmative  act  of  mind.  Thought, 
on  this  view,  selected  the  common  characteristics  in  several 
objects,  and  tied  them  up  in  a  separate  bundle  with  an  existence 
and  meaning  of  its  own.  But  it  is  more  accurate  to  speak  of 
abstraction  as  the  result  of  negative  thought.  The  abstract  or 
general  we  get,  not  by  attending  to  wliat  is  like  in  several  objects, 
but  in  neglecting  what  is  unlike.  A  great  deal  of  the  difficulty 
that  hangs  about  this  subject  would  be  removed  if  we  observed 
the  distinction  between  having  and  possessing  an  idea.  It  is  one 
thing  merely  to  have  an  idea  and  quite  a  dilferent  thing  to  have 
it  as  your  own — to  possess  it — that  is.  to  have  it  in  relation  to 
other  ideas.  It  is  the  old  familiar  distinction  between  cognition 
and  recognition. 

II 

The  o])ject  of  description  must  bo  an  object  in  relation.  T'nre- 
lated  objects  are,  as  Ilegel  rightly  saiil,  indescribable;  they  can- 
not even  be  named.  The  attributes  in  terms  of  which  I  describe 
any  object  immediately  presented  to  consciousness,  are  all  of  them 
expressions  of  the  relations  of  the  presented  object  to  objects  not 
now  present — that  are  elsewhere  in  space  and  time.  Descriptive 
judgment  must,  therefore,  always  be  conceptual  or  representa- 
tive. If  there  were  only  one  object  in  existence  we  should  not 
need  a  name  for  it,  although  we  might  need  a  word  to  distinguish 
between  the  existence  and  the  non-existence  of  this  single  object. 
Naming  is  an  act  that  belongs  to  the  world  of  exposition  and  com- 
munieation.  We  attach  labels  or  names  to  objects  only  for  the 
purpose  of  distinguisliiiii^  tlicin  from  otlier  objects. 


38  FOOTNOTES  TO  FORMAL  LOGIC 

But  prior  to  our  knowledge  of  the  object  as  described,  we 
know  the  object  as  merely  apprehended.  There  is,  to  be  sure, 
serious  objection  to  saying  that  we  know  the  object  in  this  first 
simple  awareness.  The  word  know  is  full  of  all  sorts  of  ambigui- 
ties and  it  is  one  of  the  purposes  of  these  studies  to  isolate  some 
of  its  meanings.  When  we  say  that  we  know  the  object,  in  both 
common  and  technical  usage,  we  mean  that  we  are  not  only  aware 
of  it,  but  that  we  are  aware  of  it  in  its  describable  relations. 
Knowing  is  a  relating  activity.  But  it  is  quite  impossible  to  find 
a  word  that  will  perform  any  less  ambiguously  the  self-contra- 
dictory task  of  connoting  the  absence  of  connotation.  However, 
there  can  be  no  doubt  about  the  fact. 

The  expression,  immediate  consciousness  which  is  often  em- 
ployed to  describe  this  primitive  datum  of  knowledge,  stands  for 
a  mental  state  that  is  already  well  along  toward  the  stage  of 
description  by  means  of  relations.  The  word  consciousness  itself, 
etymologically  at  any  rate,  connotes  a  togetherness.  But  it  is 
very  important  to  distinguish  between  internal  and  external 
relatedness.  "We  shall  insist  that  this  first  direct  awareness  brings 
to  us  knowledge  of  isolated  concrete  wholes,  within  which  we  see, 
or  appreciate,  or  know  qualities  in  relation. 

It  must  be  repeatedly  emphasized  that  the  state  of  mind  that 
has  now  so  often  in  Logic  and  Psychology  been  called  simple 
apprehension  is  one  of  just  pure  acceptance  or  acknowledgment. 
It  is  a  psychic  experience  in  which  there  is  no  distinction  between 
our  apprehending  the  object  and  the  object  which  is  apprehended. 
Psychologists  and  logicians  have  been  pretty  much  of  one  mind  on 
this  point,  but  there  has  been  little  agreement  upon  a  word  to  set 
forth  the  mental  state  itself.  Hobhouse  has  described  the  general 
characteristics  of  immediate  consciousness  of  a  fact  by  the  word 
assertion;  this  has  somewhat  released  the  fact  so  known  from 
being  related  to  other  facts.  But  the  word  assertion  has  now  too 
often  been  employed  as  a  synonym  for  affirmation  to  warrant 
its  being  transferred  to  this  primitive  awareness  or  pure  recep- 


AI'l'llHIIKSSIOX,  QCKSTIOS  AS  I)  ASSEiniOX  39 

tivily.  And  doubllcss  llir  same  oljji'clioti  coulil  \»-  made  to  llie 
term  acceptance ;  tlie  latter,  however,  is  fre«;r  from  tlie  notion  of. 
activity,  or  decision.  The  expression  "assertion  of  the  object" 
already  suggests  that  thought  has  gone  out  to  meet  the  object 
with  question,  criticism,  and  decision.  I  think  the  word  acknowl- 
edge is  the  most  satisfactory  foi-  this  primitive  state  of  conscious- 
ness. In  letter  writing  we  distinguish  between  acknowledging  and 
answering  a  letter.  So  when  the  mind  receives  its  facts  it  may 
just  acknowledge  them,  it  need  not  go  further  and  reply  to  them.- 

Every  fact  is,  indeed,  i-ehited  to  otlier  facts  in  tlie  real  woi-ld, 
l)ut  I  need  not  know  this  in  ordei*  to  pi'ochiim  my  accei)tance  of 
one  of  the  related  facts  as  an  isolated  tiling.  I  can  take  it  at  its 
face  value ;  I  can  bow  my  acceptance  or  acknowledgment  of  it. 
When  I  mefel_\-  conlciiiplale  the  I'ed  rose,  tliat  is,  wlieii  I  ajipce- 
hentl  it  simply,  I  (ichiioivlcdgc  something  immediately  pi'eseiit, 
and  nothing  more.  I  am  aware  of  the  red  color,  but  am  not  aware 
of  the  relation  of  the  red  color  to  anything  else.  AVhen  1  say,  the 
tree  in  my  garden  is  tall,  I  am  undoubtedly  describing  tiie  object 
by  means  of  its  relation  to  other  objects.  I  am  also  quite  truly, 
although  not  so  obviously,  describing  the  tree  through  its  rela- 
tions when  I  say  the  tree  is  green.  But  such  description  is  sub- 
sequent to  mere  apprehension,  and  is  always  in  the  interest  of 
connnunication.    The  descriptive  judgment  functions  socially. 

The  apprehended  content  cannot  contain  the  relation  of  the 
object  api)reliended  to  any  otlier  object.  It  merely  envisages  its 
own  system  of  inner  relations.  In  looking  at  a  net  from  a  dis- 
tance. I  can  be  aware  of  the  knots  without  thinking  of  the  threads 
that  run  from  knot  to  knot.  I  can  gaze  at  the  star,  Sirius,  con- 
template, accei)t,  ach-naich  <I<j(  it  without  consciously  relating  it 
to  other  stars.     r>ii1  as  soon  as  1  wish  to  describe — that  is.  com- 


-  The  critical  aiialvsis  of  the  tliinkiiii^  ]iroccss  liail  rcvcaleil  oven  to  the 
Greek  logicians  tlie  two  factors  of  apj)rehonsioii  and  assertion  in  every 
judgment.  Tliey  distinguish  clearly  between  KardOecns  and  ot^Kara^ecrts. 
These  two  asjx'cts  of  the  judging  i-onsciousiu'ss  are  also  recognized,  it  seems 
to  nu',  in  the  distinction  hetween  iirthi'iliii  and  Ik  urtln  ilm ,  which  several 
moiicrn    wiiters  lunc   iirojiosiMl. 


40  FOOTNOTES  TO  FOEMAL  LOGIC 

municate  to  my  fellows — what  I  have  thus  apprehended,  I  must 
betake  myself  to  the  discovery  of  the  relation  of  Sirius  to  other 
heavenly  bodies.  Every  description  of  an  object,  of  course,  pro- 
ceeds always  by  means  of  relations;  but  the  object  so  described 
was  undoubtedly  already  present  as  an  unrelated  fact.  It  was 
once  merely  acknowledged.  To  accept  or  acknowledge  the  fact 
is  one  thing,  to  describe  it  another. 

Now  it  is  not  until  we  arrive  at  the  steige  of  description  that 
we  may  properly  speak  of  the  psychical  process  as  judgment.  The 
mental  state  which  I  have  here  called  acceptance,  or  acknowledg- 
ment, has  often  been  described  as  inchoate  judgment,  or  sensory 
judgment.  There  can  be  no  serious  objection  to  such  an  account 
of  this  primitive  stage  of  acknowledgment  provided  we  keep  in 
mind  the  real  difference  between  it  and  true  judgment.  At  the 
second  stage  we  have  the  possibility  of  error.  In  simple  appre- 
hension, or  acknowledgment,  there  is  no  question  of  truth  or 
falsity,  and  hence  no  possibility  of  error.  The  object  presents 
itself  and  we  accept  it  without  comment.  Moreover,  the  object 
of  an  unquestioned  simple  apprehension — an  acknowledgment 
ivitlioui  comment — is  always  unalloyed  fact,  that  is,  fact  present 
and  unembarrassed  by  attachment  to  any  fact  not  present.  We 
can  make  no  mistake  in  such  an  acknowledgment  or  acceptance. 
It  is  only  when  we  comment  upon  the  acknowledged  fact,  when 
we  venture  out  along  the  relations  of  the  present  fact  to  other 
facts  not  now  present  that  error  arises.  But  then  we  are  no  longer 
merely  apprehending  the  object  we  are  making  a  judgment  about 
it.^  We  must  distinguish  therefore  between  assertion  without 
comment  or  risk,  that  is,  just  acceptance  or  acknowledgment,  and 
assertion  with  the  risk  that  accompanies  the  necessity  of  selecting 
from  competing  alternatives.     The  latter  is  true  decision,  it  is 


3 1  cannot  therefore  agree  entirely  with  Bosanquet  that  ' '  being  dis- 
tinctly aware  of  reality  is  another  name  for  judgment."  (Essentials  of 
Logic,  p.  40).  If  we  should  make  use  of  the  well-known  distinction  between 
clear  and  distinct  knowledge,  of  Descartes  and  Leibnitz,  in  which  distinct- 
ness points  inward  and  clearness  outAvard,  we  might  say  that  being  clearly 
aAvare  of  reality  is  another  name  for  judgment,  and  being  distinctlii  aware 
of  reality  is  another  name  for  the  simple  apprehension  as  I  view  it. 


Al'fUKIIKSSIOS.  QUESTION  AND  .tSSKIlTION  41 

affirmation  or  denial.  As  Ilegel  has  said,  to  assert  that  a  carriage 
is  passing  the  house  is  not  a  judgment  unless  we  are  in  doubt 
whether  it  is  a  eari-iagc  oi-  a  cart. 

It  has  been  doubted,  and  with  reason,  whether  we  can  ever 
entertain  a  significant  simple  apprehension  without  decision.  It 
must  be  admitted,  that  as  occurrences  in  a  continuous  psycho- 
logical pi'ocess,  apprehension  of  fact  and  decision  concerning  it 
are  insei)aral)ly  connected.  They  are,  nevertheless,  logically  dis- 
tinguishable. In  our  normal  adult  life  any  longitudinal  section 
of  consciousness  would  reveal  a  highly  complex  mental  state.  We 
should  never  find  in  such  cross-sections  of  the  stream  of  conscious- 
ness, at  fir.st  apprehension  and  then  judgment.  Both  would 
appear  in  each  and  every  cross-section.  And  we  can  take  thought 
about  any  one  of  tlie  elements  in  the  complex  content  only  by 
abstracting  from  the  real  organic  process  itself.  The  two  acts, 
apprehension  and  judgment,  though  theoretically  separable  are 
joined  in  one  concrete  state  of  consciousness.  We  do  not  first 
find  apprehension,  and  then  decision  and  then  action.  All  normal 
waking  consciousness  is  one  continuous  affirmation,  and.  witliin 
this  persistent  judgment,  simple  apprehension  is  seen  to  be  a 
distinguishable,  though  not  a  separate  element.  Moreover,  it 
must  not  be  supposed  that  the  two  aspects,  apprehension  and 
judgment,  merge  by  imperceptible  gradations  one  into  the  other. 
We  have  already  seen  the  true  differentia.  Simple  apprehension 
is  naive  in  its  attitude  toward  the  apprehended  fact,  judgment 
comes  with  the  discovery  that  the  observed  fact  might  have  been 
different. 

Midway  between  immediate  awareness — tlie  primary  datum 
of  knowledge — and  tlie  full-blown  judijnunt,  there  is  found  the 
impersonal  judgment.  This  type  of  judgment  has  caused  much 
trouble,  but  only  to  those  logicians  who  set  up  arbitrary  and 
impassable  barriers  l)etween  the  different  compartments  of  mind. 
There  is  no  especial  <liffieulty  in  understanding  the  impersonal 
on  the  view  that  regnrds  all  waking  consciousness  as  an  organic 


42  FOOTNOTES  TO  FOBMAL  LOGIC 

whole,  and  that  tliinks  of  the  concept,  the  judgment  and  the 
syllogism  as  the  varying  degrees  of  explicitness  in  which  this 
whole  expresses  itself.  Much  of  the  controversy  in  the  history 
of  Logic  about  impersonals  would  have  been  entirely  removed 
if  the  distinction  between  the  judgment  and  the  proposition  had 
always  been  distinctly  recognized.* 

Now  there  can  be  little  objection  to  the  assumption — and 
obviously  it  must  forever  be  an  assumption — that  the  earliest 
states  of  consciousness  in  the  development  of  the  individual  mind, 
are  of  this  undifferentiated  character.  In  childhood,  and  per- 
haps in  the  animal  consciousness,  we  find  simple  awareness  the 
sole  content.  There  is  more  difficulty  in  the  view  that  we  may 
again  relapse  into  this  level  of  simple  awareness,  from  our  later 
normal  adult  consciousness,  in  which  we  are  cognizant  of  the 
distinction  betw^een  subject  and  object,  the  self  and  the  non-self. 
Bradley  is  certain  that,  both  prior  to  and  subsequent  to  the  stage 
of  consciousness  in  which  there  is  a  distinction  between  subject 
and  object,  there  is  a  stage  in  which  we  are  not  thus  aware  of 
the  distinction  between  what  is  known  and  the  knower  thereof. 
We  are  quite  justified,  it  would  seem,  in  our  inference  as  to 
animal  intelligence  from  our  own  human  experience  of  the  stream 
of  ideas,  or  reverie. 

It  is  in  one  sense  wrong  to  call  simple  apprehension  the 
primary  operation  of  the  mind.  In  describing  simple  apprehen- 
sion as  the  primary  datum  of  knowledge  I  have  pointed  out  that 
the  terms,  earlier  and  later,  are  out  of  place  in  any  account  of 
the  relation  of  judgment  to  simple  apprehension.  Every  imme- 
diate apprehension  is  simultaneous  with  a  judgment  and  every 
judgment  with  an  apprehension. 

There  is  a  point  of  importance  that  must  now  be  noted.    We 


*  I  think,  for  example,  that  Coutnrat,  who  is  otherwise  very  mindful 
of  this  distinction,  has  ignored  its  importance  in  his  discussion  of  the 
impersonal  proposition.  He  says:  "7i  rains  is  an  indeterminate  and  incom- 
plete judgment.  This  example  shows  us  at  the  same  time  that  there  are 
judgments  without  terms,  without  subject  or  attribute."  Ency.  FhiJos.  Sci., 
I,  1.39. 


Al'I'UKlIKSSIOS,  QfESTIOX  AS  I)  ASSEimoN  4:i 

have  seen  how  jiid^iiii'nt  1  rjiiisci'iids  .siiiii)lc  aiipit-lii'iisioii  by 
iii(|uifiii}^  into  tlic  outer  foi'tuucs  of  tlic  ai)pf<'lH'ii(lc(l  faet  and 
discovering  its  external  relations.  As  merely  ajjpreliended  the 
fact  was  unequivocal ;  it  was  an  innnediate  f(;eling,  a  knowing 
and  being  in  one.  But  now  the  discovery  of  the  relations  of  the 
apprehended  fact  to  its  fellow  facts  in  tlie  objective  order  is  the 
discovery,  also,  tliat  each  of  these  relations  might  have  been 
diflferent.  Thought  has  thus  ti-anseended  the  unambiguous  simple 
acknowledgment  of  fact.  But  in  passing  to  this  higher  stage  of 
decision,  or  judgment,  that  is,  the  stage  of  selection  from  among 
possible  relations,  the  original  simple  apprehension  does  not  dis- 
appear; it  remains  continuously  in  view  as  the  foundation  of  the 
later  selective  knowledge.  Immediate  awareness  is  not  a  stage 
that  appears  and  then  disappears. 

Ill 

It  will  not  be  out  of  i)laee  to  pui-sue  this  analysis  a  step 
further.  Can  we  not  discover  a  stage  in  tlie  coinidex  content  of 
consciousness  prior  to  apprehension?  Do  we  not  first  have  the 
fact  in  the  experience  of  one  moment  and  then  in  a  subsequent 
moment  apprehend  it?  Such  a  distinction  has  been  made.  It 
has  been  held  that  to  he  in  consciousness  and  to  be  apprehended 
are  not  identical  stages,  that  mere  presence  in  consciousness 
does  not  imply  even  in  the  faintest  degree  the  subject-object 
relation,  while  in  apprehension  the  relation  of  consciousness  to 
the  presented  fact  has  for  the  first  time  become  explicit.  But, 
in  my  oi)inion,  this  is  a  refinement  of  distinction  that  cannot  be 
defended.  To  be  in  consciousness  and  to  be  apprehended  as  being 
in  consciousness  are  identical  facts,  and  both  postulate  the  sub- 
ject-object relation.  The  content  of  simple  apprehension  is  non- 
relational but  this  does  not  exclude  internal  variety  in  the 
content  itself.  Tliis  innnediate  awareness  unrelated  in  itself 
but  yet  embosoming  distinctions  is,  I  believe,  wliat  Bradley  has 
continually  spoken  of  as  "feeling." 


44  FOOTNOTES  TO  FOEMAL  LOGIC 

It  has  been  urged  as  an  objection  to  every  sueli  analysis  of 
the  logical  content  of  consciousness  that  it  hopelessly  confuses  the 
psychological  with  the  logical  point  of  view.  Logic,  it  is  said, 
demands  real  distinctions — definite  lines  of  demarcation.  But 
I  see  no  reason  for  contending  that  logical  consciousness  is  any 
more  definite  in  its  entire  content  than  is  psychological  conscious- 
ness. We  do  not  go  wide  of  the  mark  when  we  say  that  the 
logical  apprehensions,  like  the  psychological  sensations  shade  by 
imperceptible  gradations  from  explicit  to  implicit  and  vice  versa. 
The  content  of  sensation  has  its  focal  point  of  greatest  clearness 
from  which  it  fades  away  to  a  zero  point  of  indefinitness ;  also, 
we  apprehend,  or  comprehend,  or  know  by  means  of  the  concei)t, 
the  judgment,  or  the  syllogism  in  varying  degrees  of  explicitness 
of  the  content. 

We  must  insist  again  that  this  immediate  experience  does 
not  represent  a  stage  in  the  psychical  development  which  is  at 
one  time  jiresent  and  necessary  and  later  disappears.  When  the 
discrimination  between  the  self  and  the  non-self  has  arisen  and 
we  find  the  relational  type  of  consciousness,  this  primary  aware- 
ness must  still  be  a  felt  aspect  of  the  whole  content.  As  Bradley 
has  said,  "all  that  is  thus  removed  is  the  mereness  of  immediacy." 
The  one  point  which  I  wish  to  repeat  with  especial  emphasis  is 
that  it  is  an  error  to  suppose  that  our  conscious  contact  with 
the  world  of  objects  starts  with  judgment.  Reality  has  been 
presented  to  mind  in  its  first  simple  awareness— the  object  has 
been  accepted  as  a  constituent  datum  of  knowledge.  The  expres- 
sion "a  mere  suggestion"  hints  at  this  stage  of  simple  appre- 
hension Avhere  fact  has  been  accepted  without  affirming  it. 

It  would,  perhaps,  be  a  more  precise  account  of  the  primitive 
datum  of  knowledge  to  call  it  an  inner  movement  of  analytic 
attention  confined  entirely  to  an  immediately  presented  fact. 
But  we  should  guard  against  the  mistake  of  thinking  that  in 
this  earliest  stage  of  consciousness  any  act  of  classification  is 
involved,  for  this  would  imply  a  comparison  with  other  facts  not 


Ai'i'i!i:iih:ss]()\,  (jrF.srios  asd  AssF.irrios  4r, 

now  present.  We  must  also  (listiii<^uisli  Ix'tweeii  tlic  judgiiient 
to  wliicli  We  have  passed  in  proceeding  oiilw;wdl>'  to  a  classifica- 
tion of  the  given  fact  with  other  not-given  facts,  and  the  gronnd 
of  tills  judgment.  Tlieoi'etically  at  least,  we  may  say  that  tiie 
gi'onnd  varies  from  tiic  zero  i)oint  of  complete  indifference,  or 
unmotived  assertion,  to  complete  conviction,  or  internal  self- 
suflicing  satisfaction.  But  now,  this  stage  of  ajipi-ehension,  which 
we  are  attempting  to  fix,  is  at  a  level  below  the  zero  of  sheer 
doubt.  The  doubt  is  always  a  decision  not  to  decide.  Apprehen- 
sion, however,  has  not  even  this  characteristic,  for  here  we  have 
just  the  self-revelation  of  the  inner  content  of  the  datum,  and 
al)out  that  there  is  no  doubt. 

It  will  be  seen  that  this  account  of  the  relation  between  appre- 
hension and  judgment  is  in  close  agreement  with  Wundt's  theory 
that  all  judgment  in  the  last  analysis  involves  an  act  of  will. 
Professor  Adamson  has  challenged  this  view,  asserting  that  judg- 
ment requires  no  reference  to  reality  beyond  the  "sensible  press- 
ure,"' that  it  is  just  the  belief  in  the  existence  of  the  objects 
from  which  the  sense  perception  issues.  Judgment,  he  says, 
"requires  in  addition  to  the  belief  that  something  exists,  no  con- 
sideration as  to  whether  the  belief  itself  be  true."  This,  I  think, 
is  a  doctrine  that  is  opposed  to  fact.  In  our  account  every  judg- 
ment calls  for  a  decision  as  to  the  validity  of  the  fact.  In  this 
state  of  consciousness  that  Professor  Adamson  has  described  as 
already  the  beginning  of  judgment,  we  have  only  analytic  atten- 
tion to  the  pressure  from  the  sense-presented  fact,  not  analytie 
judgment. 


CHAPTER   III 

THE  IMPORT  OF  JUDGMENT 

I 

The  various  questions  about  the  nature  of  judgment — the 
relation  of  subject  to  predicate,  of  percept  to  concept,  of  analysis 
to  synthesis,  of  form  to  matter — all  presuppose  that  the  word  is 
has  one  well-defined  meaning.  But  the  problem  of  the  copula  is 
beset  with  world-old  difficulties.  Russell,  who  is  always  tem- 
perate in  his  statements,  has  said,  ''Is  is  terribly  ambiguous,"^ 
and  has  pointed  out  five  quite  different  meanings.  And 
DeMorgan  before  him,  with  his  eagle's  eye  for  paradoxes  and 
ambiguities  remarked :  ' '  The  complete  attempt  to  deal  with  the 
term  is  would  give  the  grand  cyclopedia,  and  its  yearly  supple- 
ment would  be  the  history  of  the  human  race  for  the  time."- 

It  will  not  be  necessary  for  our  present  purpose  to  go  far  into 
the  subtleties  of  these  modern  discussions  of  the  meanings  of  is. 
It  should  be  pointed  out,  however,  that  these  ambiguities  are  not 
new  discoveries.  Aristotle  was  fully  aware  of  the  unavoidable 
ambiguity  in  any  word  that  is  made  to  serve  as  connecting  link 
betw^een  subject  and  predicate  in  judgment.  Following  his 
teacher,  he  spoke  most  often  of  the  relation  between  the  world 
of  concrete  things  and  the  world  of  ideas,  which  is  expressed  in 
the  judgment,  as  one  of  participation.  And  for  twenty-three 
centuries,  from  Aristotle  to  Bradley,  the  expression  "participate 
in"  has  been  condemned  for  its  metaphorical  vagueness  and 
ambiguity.  The  important  thing  to  be  borne  in  mind  is  that  at 
heart  it  is  always  the  same  relation,  whether  we  say  that  a  thing 


''^Principles  of  Mathematics  (Cambridge,  Uuiversity  Press,  1903),  I,  p.  64. 
2  Formal  Logic  (London,  Taylor,  1847),  p.  49. 

[46] 


Till-:  iMi'o/rr  of.udcment  47 

is  a  vopi)  of  till'  idea,  oi'  thai  it  jxirlicipatcs  in  it,  oi'  tiiat  it  is 
the  idea.  And  tlic  essential  eliai-acteristic  of  this  relation 
between  subject  and  predicate  in  judgment  is  that  it  is  non- 
temporal.  This  fact,  namely,  that  the  relation  is  not  in  time, 
while  the  relata  are,  will  receive  fuller  elucidation  in  the  sequel. 
It  is  for  the  reason  tliat  the  time  element  is  l)oth  in  and  around 
the  judgment  that  some  pai-t  of  the  verb  to  be  has  always  been 
preferred  to  express  the  relation  between  subject  and  predicate. 
As  has  so  often  been  pointed  out,  if  there  were  no  reason  why 
the  verb  to  he  should  ])e  used  as  tlie  sign  of  predication  it  would 
be  difficult  to  explain  its  presence  in  so  many  languages. 

Among  the  nuuiy  meanings  of  in,  its  existential  import  should, 
of  course,  be  considered  first.  The  cop^ila  jf  ^^1^^  pr^pngitiAn 
8  is  P,  in  the  first  instance,  stands  for  the  fact  that  in  every 
judgment  there  is  undeniably  present  to  consciousness  a  some- 
Thing.  IloVn'vei-  widely  tiiey  may  differ  in  other  ways  all  theories 
of  ])redieation  ai'e  agreed  upon  this  i)oint.  We  are  not  now  inter- 
ested in  the  question  whether  this  affirmation  of  presence  is  of 
something  present  to  consciousness  or  in  consciousness,  that  is, 
whether  it  is  to  be  regarded  as  a  datum  or  ideatum.  T]if  ''pre- 
sence"  characteristic  of  is  must  he  taken  as  original — ^it  is  not 
derived  fronj  or  constituted  out  of  relations  between  the  presented 
object  itself  and  another  ol)je('t.  It  lias  no  temporal  origin.  The 
present  which  is  assected  in  the  judgment  is  iioi  a  smnnchat 
coming  after  a  ])riori  past.  Nor  is  it  to  be  defined  as  the  imagiti- 
ai-y  line  of  denuireation  between  the  past  and  the  future.  The 
present  is  not  that  which  comes  after  something  past,  but  the 
past  is  something  which  came  before  the  present,  /sstanils 
always  as  the  reminder  that  knowledge  is  won  l)y  the  extension 
of  the  present. 

It  is  no  dis])arageinent  of  tlie  underived  validity  oi  X\n^  pn  Si  nt 
to  show,  as  may  be  sliown,  lliat  we  liave  not  achieved  knowledge 
until  we  have  thus  expanded  the  present  into  its  relation  with 
things  other  tlian   its(df.     Tf  thought  were  eonfined  strictlv  to 


48  FOOTNOTES  TO  FORMAL  LOGIC 

the  present  it  would  not  know  it,  and  we  sliould  never  Ije  impelled 
to  judge.  In  judgment  the  present  yields  to  the  internal  con- 
straint to  transcend  itself.  But  the  apprehension  of  the  present 
and  the  effort,  in  judgment,  to  pass  beyond  the  present  must 
not  be  confused.  They  are  different  acts.  The  present  as  imme- 
diately apprehended  is  singular — it  is  a  Uiis  unrelated  to  any 
that.  But  as  a  this  it  is  the  unification  of  its  own  unique  attri- 
butes; as  apprehended  fact  it  owes  no  allegiance  to  its  other. 
But  knowledge  of  this  as  distinguished  from  its  eippreh.ension 
does  require  an  insight  into  the  relations  of  the  this  to  the  that. 
The  system  of  Hegel  dift'ers  from  other  idealistic  philosophies 
on  the  question  of  the  time  factor  in  judgment.  Hegel  discredits 
immediate  consciousness,  declaring  that  the  conception  of  immed- 
iacy breaks  down  under  the  strain  of  its  own  inherent  self- 
contradiction.  I  can  apprehend  an  object  presented  to  conscious- 
ness in  one  act  and  in  a  second  act  of  thought  I  can  be  aware  of 
the  first  state,  but  not  as  iuunediately  present.  I  cannot  think 
that  I  think,  I  can  only  think  that  I  thought.  But  this  does  not 
seem  to  me  to  be  a  valid  objection  to  immediacy  of  consciousness. 
It  is  true  that  we  can  never  communicate  descriptively  the  present 
state  of  consciousness  without  judging  and  thereby  causing  the 
present  to  slip  away  from  itself  into  the  past.  The  second  act. 
indeed,  is  not  immediate  in  the  same  sense  as  the  first  act.  When 
I  say  "I  think  that  I  thought,"  the  "I  thought"  which  is  the 
object  of  "I  think"  is,  indeed,  other  than  that  which  thinks  it, 
but  otherness  is  here  unjustifiably  construed  as  equivalent  to 
past.  The  Hegelian  recourse  to  memory  is  unnecessary.  Intro- 
spection, I  think,  will  also  discover  that  memory  plays  no  such 
part,  as  Hegel  thought.  When  we  examine  the  thought  that  has 
this  i)ossession  of  an  immediate  content,  we  do  not  find  in  it  any 
act  of  remembering,  as  this  doctrine  declares.  The  mind  seems 
truly  to  be  noting  something  which  is  present  to  it  then  and 
there.  "What  I  feel"  says  Bradley,  "that  surely  I  may  still 
feel  though  I  also  at  the  same  time  make  it  into  an  object  before 


rilK  IM I'dirr  OF.II  hCMKNT  49 

me."  None  of  the  vai'ioiis  words  lliat  arc  eoinpoiUKled  with  self — 
self-consciousness,  self-contemplation,  self-reproach,  etc. — sug- 
gests a  combination  of  the  present  with  i-emembered  aspects  of 
itself.  Suhjeet  and  object  are  both  in  the  same  present  time. 
This  is  illustrated  in  the  humorous  poem  the  first  line  of  which 
I'uns  "Says  I  to  myself,  says  I." 

It  is  true  that  the  complex  content  of  immediate  consciousness 
may  experience  one  aspect  of  itself  to  be  more  vividly  present 
than  another.  But  these  remote  or  less  vivid  aspects  are  not 
therefore  to  be  relegated  to  the  i)ast.  Differences  in  the  "felt 
immediacy"  are  like  the  differences  in  the  marginal  vision  of  the 
eye.  They  are  all  present  in  varying  degrees  of  definiteness. 
T  can  not,  obviously  turn  the  whole  content  of  consciousness  into 
an  object  at  once.  A  part  of  the  self  must  be  held  in  reserve, 
so  to  speak,  to  be  the  experiencing  subject  of  the  part  that  has 
taken  its  place  as  object  to  be  exi)erieneed.  And  the  line  of 
cleavage  witliin  the  whole  content  may  differ  for  different  pur- 
poses. Also  the  sameness  of  the  parts  does  not  exclude  differ- 
ences. In  the  line  ' '  Says  I  to  myself,  says  I, ' '  the  person  speak- 
ing and  the  person  addressed  are  the  same  and  yet  obviously 
different,  for  the  better  self  is  addressing  the  evil  self. 

It  is  important  in  discussing  the  meaning  of  is  to  distinguish 
between  being  and  existence.  Every  conceivable  thing,  every 
object  of  thought  has  its  being,  lint  not  all  have  existence.  The 
i^ijninium  requisite  of  being  is  tlic  (|uality  of  inmilxi-.  Anything 
that  can  be  thought  of  as  having  membership  in  llic  number 
series  has  the  (piality  of  being.  But  tliin<>'s  liavc  i.rish  m-i  only 
if  they  "stand  out""  in  systems  of  s[  ire  in  I  iiiti'i--icl;ii  iiuiship.  We 
may  deny  the  existence  of  anything  onl\-  if  we  are  able  to  save 
its  being.  Contradictory  as  it  may  seem  we  must  say  that  what 
does  not  exist  must  still  he  something.  The  assertion  ^'S  is  not" 
is  on  the  one  sick-  either  entirely  false,  or,  on  the  othei".  more  than 
idle — just  empty  breath.  If  /S'  were  just  nothing  at  all,  it  would 
be  meaningless  to  say  "^S*  is  not."    Bdng  is  the  general  attribute 


50  FOOTNOTES  TO  FORMAL  LOGIC 

that  belongs  to  anything  that  can  stand  as  suljject  of  a  proposi- 
tio2i.  This  truth  was  expressed  in  an  earlier  paragraph  in  the 
statement  that  in  every  judgment  there  is  unmistakably  present 
to  thought  a  something.  The  judgment  "  S  \^P,"  means  to  assert 
that  reality  has  the  characteristic,  8-P:' 

II 

In  considering  the  nature  of  the  concept  or  idea  we  saw  that  it 
is  difficult  to  discover  any  difference  in  kind  among  the  cognitive 
states  of  consciousness,  from  simplest  concept  to  the  most  com- 
plex judgment.  That  the  concept  seems  to  shade  by  imperceptible 
gradations  into  the  judgment  was  recognized  by  Aristotle  and 
before  him.  And  in  the  modern  discussions  we  find  writers  who, 
having  defined  the  concept  and  the  judgment  in  static  terms, 
in  independence  of  each  other,  are  much  embarrassed  by  the 
discovery  of  forms  of  thought  that  refuse  to  be  classed  as  either. 
There  are  forms  which  have  already  burst  the  conceptual  shell 
and  yet  are  classed  as  concepts ;  and,  on  the  other  side,  there  are 
forms  wliich  are  classed  as  judgments  that  are  lacking  in  the 
essentials  of  judgment.  The  recognition  of  this  distinction  led 
Bain  to  call  the  verbal  proposition  the  "notion  in  the  guise  of  a 
proposition." 

Nevertheless,  when  one  describes  thinking  as  a  movement 
from  the  particulars  of  concrete  sense  experience  to  conceptual 
universals,  he  disregards  a  most  important  aspect  of  the  knowing 
process.  In  its  analytic  attention  thought  makes  distinctions  (or 
we  should  say,  heightens  distinctions  already  vaguely  present), 
and  these  distinctions  when  synthesized  form  the  generals.  But 
this  is  only  one-half  of  the  process.     These  abstractions  which 


3  Plato  long  ago  pointed  out  the  paradoxical  fact  tliat  when  you  call 
a  thing  a  non-entity,  a  mere  illusion,  you  do  not  thereby  get  rid  of  it. 
There  is  a  deep  metaj^hysieal  significance  in  the  remarks  of  the  colored  man 
passing  by  a  church  yard  at  night :  "I  don 't  belie%'e  in  ghosts  nohow, 
but  I  hope  they  never  find  it  out,  it  might  make  them  mad  to  think  a  fellow 
didn  't  believe  in  them. ' ' 


TIIF.  IMI'Oirr  OF  .Jl'IX'.MKNT  51 

lie  at  the  end  of  the  niovenient  in  this  direction  are  not  kept  in 
cold  storage,  l)iit  ai'f  tlirown  back  a^ain  upon  the  concrete 
instances  from  which  tliey  arose.  And  in  tliis  return  movement 
the  coneej)ts,  or  universals,  always  put  a  new  meaning  into  the 
concrete  instances.  Nevertheless,  in  this  reciprocating  movement, 
thought  is  not  acknowledging  its  inadequacy  to  reality.  This 
is  not  a  make-shift,  or  compi'omise,  confessing  thought's  incom- 
petence :  it  is  an  exhibition  of  tlie  highest  type  of  control  of 
reality.  A  transverse  cross-section,  so  to  speak,  of  the  movement 
would  reveal  the  seeming  contradictions  of  idleness  and  falsi- 
fication. Any  moment  of  the  process  would  exhibit  tautology,  or 
novelty,  when  detached  from  its  setting  in  the  whole.  But  a 
longitudinal  section  would  reveal  the  true  nature  of  the  process 
in  its  totality,  where  the  tautology,  in  the  light  of  the  anticipated 
novelty,  is  not  to  be  condemned  as  idle ;  and  the  novelty,  resting 
back  on  the  identity,  rescues  the  judgment  from  the  charge  of 
falsity. 

As  hearing  upon  our  search  for  the  essence  of  judgment  we 
may  revert  to  the  significant  distinction  that  has  often  been  made 
between  hnowing  and  understanding.  It  is  alleged  that  we  are 
here  dealing  with  thought  processes  that  are  sufficiently  different 
to  require  two  ditf.erent  words.  Understanding  is  a  later  and 
and  higher  phase  of  flunking.  We  have  understanding  when  Ave 
appreciate  or  evaluate  knowledge,  when  wc  know  that  we  know, 
and  why  we  know.  Although  the  distinction  between  the  two 
kinds  of  knowledge  has  frequently  been  pointed  out,  there  has 
not  been  offered,  it  seems  to  me,  a  convincing  account  of  their 
relation.  Bearing  in  mind  tliat  tlicse  words  represent  stages  in 
the  development  of  knowledge,  and  therefore  have  something 
in  common,  the  question  at  issue  in  the  relation  between  the  two 
types  of  knowing  is  What  precisely  have  they  in  common  ?  Are 
they  different  in  kind  or  are  they,  as  lias  been  remarked,  an 
earlier  and  a  later  stage  in  wluit  is  essentially  a  simple  pi-ocess? 
That  there  are  these  two  kinds  of  mental  activities  is  evidenced 


J2  FOOTNOTES  TO  FOBMAL  LOGIC 

by  the  fact  that  most  languages  have  two  different  words  to 
represent  them:  scire  and  cognoscere,  in  Latin;  kennen  and 
ivissen  in  German;  savoir  and  connaitre  in  French,  stand  for 
these  two  kinds  of  knowing.  In  English,  in  addition  to  the  words 
knowing  and  understanding,  we  have  several  aspects  of  the  same 
distinction  expressed  in  the  phrases,  "knowledge  of  acqiiain^- 

j   ance"  and  "knowledge  about." 

It  will  be  well  to  examine  more  closely  the  ditference  that  is 
here  intended.     We  need  to  discover,  if  possible,  the  point' at 

.  which  there  is  a  change  in  kind  as  we  pass  from  the  lowest  form 
of  sensory  judgment  to  the  highest  type  of  reflective  judgment. 
Knowledge  of  things  by  acquaintance  is  not  far  removed  from 

1  Hegel's  unrelated  immediacy;  it  is  just  simple  apprehension 
or  existential  awareness.  But  now  all  who  have  ever  attempted 
to  describe  and  explain  this  simplest  forni  of  knowledge  have 
admitted  the  difficulty  in  giving  it  any.  logically  independent 
/  standing.  It  seems  to  have  no  existence  apart  from  the  higher 
knowledge,  the  knowledge  of  truth.  Even  Russell,  while  claim- 
ing logical  independence  for  the  knowledge  of  acquaintance, 
says :  "It  would  be  rash  to  assume  that  human  beings  ever,  in 
fact,  have  acquaintance  with  things  without  at  the  same  time 
knowing  some  truth  about  them."  All  that  we  seem  justified  in 
saying  is  that  we  find  these  two  distinguishable,  but  not  separable 
stages  in  the  natural  course  of  thought — first  immediate  aware- 
ness, then  being  aware  of  the  awareness.  I  can  think,  and  then  I 
can  think  or  recognize  that  that  is  one  of  my  thoughts.  The  sec- 
ond, or  complex  stage  is  the  stage  of  description,  definition,  evalu- 
ation.   But  already  in  the  first  or  simple  stage  there  are  implicit 

\  these  characteristics  which  on  the  reflective  level  have  become 

\£xplicit. 

'■'    This  distinction  between  the  two  types  of  knowing  we  have 

in    Professor    James'    familiar    illustration    of    the    difference 

between  cognition  and  recognition.     A  bird  flutters  against  my 

window  ]iane.  and  I  acknowledge  the  event  in  its  first  stage  of 


'////•;  iMi'oirr  or  .11  ncMhwr  .1:5 

imiiKMliiitc  awtifcncss  with  ■■Hello,  tliiiij^-a-hol). " "  And  in  the 
second  stage  of  evaluation  I  say,  "Ah,  robin."  IJiit  even  here, 
is  the  difference  more  than  relative?  Is  the  transition  from  one 
pulsation  of  consciousness  to  the  other  marked  by  any  difference 
in  kind?  The  fii'st  jud«i:inent  is  in  the  form  of  .S'  is  P  in  which 
thei'e  is  already  a  par-tial  (Idinition  which  the  second  judLjiuent 
S  is  P  only  makes  more  explicit. 

Some  wi'iters  suppose  tiiat  there  are  in  the  thought  process, 
more  than  the  two  stages  we  have  just  considered.  Adamson 
says:  ■'The  real  oi'dcr  is  sensation  and  sensory  judgment,  con- 
ception, memory  and  memorial  judgnuMit,  experience  and  experi- 
ential judgment,  inference,  inferential  judgment,  inferential 
conception."^  l)Ut  tlie  more  stages  one  marks  out  in  the  process 
the  more  does  one  emphasize  the  fact  that  consciousness  is  a 
single  continuous  affirnmtion  in  which  there  is  nothing  at  the 
end  of  the  pi'occss  which  was  not  alsp  pr(>sent  at  the  l)eginning. 
In  other  words,  there  is  no  distinction  between  beginning  and 
end.  We  may  read  off  the  story  of  our  analysis  in  either  direc- 
tion, thus  revealing  the  true  nature  of  thought  as  the  exhibition 
of  a  whole  through  its  genuinely  sinntltaneous  differences. ■'' 
Temporal  arrangement  in  the  proposition  is  an  entirely  different 
thing  from  logical  coherenc if .  in  the  judgment.  The  relation 
between  the  parts  of  a  logical  whole  is  unique,  it  is  altogether 
different  from  sequence  of  time  and  from  contiguity  of  space. 
Logical  coherence  has  heen  confounded   with  sequence   in   time 


■i  Encyclopedia  Britaiuiica,  XVI,  880. 

5  Cf.  Bradley,  in  Mind,  n.  s.,  XVIT  (1908),  170.  "The  content  of  the 
judgment  is  one  thing  and  its  jisychical  duration  is  another  thing,  and  in 
principle  we  have  seen  that  the  duration  is  irrelevant.  But  on  the  other 
hand  every  judgment  is  a  psychical  event  and  has  therefore  duration. 
Wliolly  to  deny  this  aspect  seems  a  fundamental  error. ' ' 

"  Cf .  Bosanquet,  Esscntiaiti  of  Lofjic  (London,  Macmillan,  189.3).  ]).  73. 
"The  separate  existence  of  the  spoken  or  written  word,  produces  an  illusion 
which  has  governed  the  greater  part  of  logical  theory  so  far  as  concerns 
the  separation  between  concept  and  judgment,  i.e.,  betAveen  entertaining 
i<leas  and  affirming  them  in  reality.  In  our  waking  life,  all  thought  is 
judgment,  every  idea  is  referred  to  reality,  and  in  being  so  referred,  is 
ultimatelv    affirmed    of    realitv. " 


54  FOOTNOTES  TO  FOBMAL  LOGIC 

and  with  contiguity  in  space,  because  in  speech  and  in  writing 
we  do  produce  mental  and  physical  symbols  su])j(^ct  to  time  and 
space.''  But  it  should  be  remarked  that  it  is  not  sufficient 
to  say  that  in  most  modern  and  highly  developed  languages,  the 
subject,  predicate  and  coi)u]a  in  the  proposition  are  separate 
words,  while  in  the  ancient  and  undeveloped  languages  they  are 
welded  together  in  a  single  form.  Some  explanation  of  the 
phenomenon  should  be  offered.  If  "I  am  loved"  is  equivalent 
to  amor,  it  would  be  interesting  and  important  to  know  what 
principle  of  evolution  has  produced  the  former  differentiated 
expression.  Is  it  entirely  a  phenomenon  in  the  growth  of 
language,  or  is  it  vitally  connected  with  certain  stages  in  the 
movement  of  tlic  judging  process  itself? 

No  judgment  can  ever  become  so  complex  as  to  escape 
embracement  in  a  single  idea.  But  the  related  parts  of  this 
enwholing  idea  are  not  themselves  just  ideas  in  relation.  Judg- 
ment is  not  merely  the  affirmation  or  denial  of  a  relation  between 
the  two  ideas.  This  has  been  pointed  out  so  frequently  in  recent 
discussions  that  I  need  only  refer  to  it  in  passing.  When  I 
assert  that  an  automobile  is  going  down  the  street,  I  do  not  mean 
that  my  idea  of  an  automobih^  is  traveling  down  my  idea  of  a 
street.  What  I  mean  to  affirm  is  that  the  objective  world  does 
have  in  it  a  complex  of  related  facts  which  I  characterize  as 
automobile-going-down-tlie-street.  But,  as  I  have  already  in- 
sisted, the  object  to  whicli  the  idea  refers  its  content  is  in  no 
wise  alien  to  that  idea.  Every  idealistic  theory  of  judgment 
must  of  course  hold  that  this  object  is  just  the  self -transcending 
character  of  tJie  idea.  What  I  wish  to  emphasize  is  the  fact  that 
the  ideas  hetween  which  the  relation  exists  are  not  the  same  in 
kind  as  the  idea  icithin  which  the  relation  is  embedded.  A  dis- 
persive category  operates  in  the  former  instance  and  a  synthetic 
category  in  the  latter. 


'/■///•;  iMi'oirr  of  .iidcmest  55 

III 

Ainoii},'  tilt'  (Iis|)ii1c<l  |>i-()l)lriiis  l\'iii<,''  oil  tin-  hoi'dri-Iini'  of 
Psyeliolog\'  and  Logic  is  the  question,  wliicli  wf  have  ali-cadN' 
noted,  of  the  din't'i'cncc  Ix'twccn  perception  and  tin-  jx'i'ceptive 
judguiciit.  liiadley  and  otiicrs  have  insisti'd  upon  the  impor- 
tance of  distinguishing  between  these  two  mental  states.  We 
have  already  discussed  one  aspect  of  this  subject.  In  pure  per- 
ception there  is  a  direct  reference  to  an  object,  which  is  a  datum 
in  the  etymological  sense  of  tiie  woi-d.  The  object  is  something 
given  to  the  subjective  activity  independent  of  that  activity.  The 
perceptive  judgment,  however,  is  an  inner  ideational  process 
proceeding  from  the  sjjontaneous  activity  of  the  subject,  in 
response  to  or  as  a  i-eaction  upon  the  perception.  The  difference 
lies  in  the  essential  distinction  between  activity  and  passivity. 
The  ultimate  object  in  every  assertion  or  enunciative  act  of  con- 
sciousness is  an  individual.  In  liu'  perceptive  judgment  this 
objective  is  given  to  thought  directly,  and  implies  the  existence 
of  two  things  only,  namely,  that  object  and  the  mind  that  thinks 
it.  But  in  the  cognitive  or  reflective  judgment  the  object — again 
an  individual — is  given  indirectly.  In  the  reflective  judgment 
the  object  is  only  vicariously  present  in  tli<'  concept,  to  which 
concept  other  like  objects  have  already  been  given  and  to  which 
future  objects  may  in  turn  be  presented.  The  transition  from 
perce]>tioii  to  pei'ee])tive  judgnu'nt  is  made  in  the  interest  of  com- 
munication. 

The  projiosition  as  the  outward  expression  of  the  inward  fact 
of  judgment  is  i)rinuii'il\'  an  instrument  of  intercourse — its  func- 
tion is  purely  social.'  It  begins  with  an  undifferentiated  whole 
in  the  position  of  subjc^ct,  and  concludes  with  this  same  whole 


"  \Viu(1(^H)anil  has  laiil  j^icut  stress  on  the  sot-ial  rliaracttT  of  kiiowiiiij. 
* '  Pere(Mviii<j  ami  kiiowiiifi, "  he  says,  "as  cmpirii-al  functions  are  entirely 
social  in  their  natun\  They  are  inteji^ral  parts  of  the  common  mental  life — 
for  the  lonely  strivings  after  truth  of  the  individual  are  a  late  product  of 
civilization  which  is  always  rooted  in  some  historical  community  of  knowl- 
edge and  tends  to  discliarge  itself  into  it  again.''     Kiifii.  PIiUds.  Sci.,  I,  ()17. 


56  FOOTNOTES  TO  FOEMAL  LOGIC 

differentiated  into  members,  one  of  which  takes  its  place  in  the 
position  of  predicate.  The  analysis  of  this  undifferentiated 
whole  is  what  the  speaker  accomplishes,  when  by  means  of  a 
descriptive,  elucidative,  or  demonstrative  judgment,  he  under- 
takes to  instruct  his  hearers — when  as  we  say  he  communicates 
information.  Now  the  logician  who  stresses  the  non-temporal 
character  of  judgment  finds  it  difficult  to  account  for  these  differ- 
ent meanings  that  are  found  at  the  two  significant  dates  in  the 
life  history  of  the  subject,  namely,  its  meaning  before  and  its 
meaning  after  the  differentiation.  The  judgment  is  thus  seen  to 
be  neither  exclusively  temporal  nor  non-temporal.  It  may  be 
both  without  contradiction. 

The  failure  to  recognize  this  fact,  namely,  that  the  judgment 
claims  to  be  both  temporal  and  non-temporal  has  thrown  the 
new  theories  into  hopeless  confusion.  The  judgment  is  not  in 
time,  but  the  judging  is.  The  judgment  in  the  speaker's  mind, 
prior  to  his  determination  to  express  its  meaning — to  tell  his 
hearers  something — is  not  in  time.  But  the  judging,  which 
unfolds  itself  outwardly  in  the  proposition  is  in  time.  The 
empirical  theories  of  judgment  have  with  right  insisted  that 
there  is  a  sense  in  which  the  judgment,  or  more  accurately  the 
judging  process  must  be  regarded  as  in  time.  But  this  temporal 
expression  of  itself  is  just  the  standing  reminder  of  the  irra- 
tionality of  sense,  or  the  ill-adaptation  of  conception  to  percep- 
tion. If  thought  WTre  entirely  adequate  to  the  task  of  communi- 
cation, it  would  not  adopt  this  apparently  self-contradictory 
device  for  its  outward  expression.  But  the  a-priorist  has  also 
rightly  insisted  that  the  judgment  (not  the  judging)  is  non- 
temporal.  It  has  no  parts  that  may  be  arranged  seriatim  like 
the  parts  of  a  sentence.  The  relation  between  subject  and 
predicate  is  not  a  relation  between  successive  mental  states,  but 
is  itself  a  unitary  progressive  state. 

Professor  Schiller  says  "We  have  steadily  kept  in  view  the 
fact  that  Judgment  is  the  primary  act  of  thought  and  that  the 


THE  iMi'oirr  ()F./ri)(;.\n-:\T  57 

atl<'iii]tt  of  l^'oi-inal  IjOj^ic  to  " analyse'  it  into  soinctliin^  more 
I'lcnicntai y  is  a  fictitious  proccdui'O,  which  can  be  justified  only 
by  its  convenience  and  success."*  Now  many  who  are  distinctly 
not  pragmatists  would  agree  entirely  with  Professor  Sehiller 
that  judgMient  is  tiie  pi'iiiiary  act  of  thought,  and  that  only  by 
abstraction  can  we  arrive  at  any  tiling  more  elementary.  Also 
in  the  majority  of  the  ordinaiy  textbooks,  where  the  first  ehap- 
tei-s  ticat  of  terms  and  ideas,  the  authors  are  careful  to  point 
out  that  such  discussions  belong  pi-operly  to  philology,  and  to 
psychology.  Even  Jevons  who  is  so  outspokenly  an  associa- 
tionist  in  his  view  as  to  the  nature  of  the  thinking  process  says: 
"Tlie  continued  study  of  Logic  convinces  me  that  this  doctrine 
of  terms  is  really  a  composite  and  for  the  most  part  extra-logical 
body  of  doctrine.^ 

Tt  is  true,  as  Aristotle  remarked,  antl  as  since  then  so  many 
logicians  have  repeated,  a  word  lias  no  reality  in  living  language, 
and  the  idea  no  reality  in  living  thouglit.  We  must  not  regard 
the  proposition  as  a  synthesis  of  words,  nor  the  judgment  as  a 
synthesis  of  ideas.  And  yet,  when  once  the  act  of  judging  has 
been  performed  a  retrospective  analysis  discovers  ideas  to  be 
diff(  r(iif,  but  )i()f  sfparafe  aspects  of  the  judgment. 

The  data  of  knowledge  appear  to  come  in  a  stream  of  isolated 
sense-pi'esented  facts,  which  the  mind  is  called  upon  to  weld 
togethei'  into  wholes  of  ever  increasing  complexity.  The 
sequence  in  the  mental  states  seems  to  be  first  the  idea  A,  then 
tiie  idea  li.  and  lastly  the  judgment  A  in  relation  to  B.  Some  of 
the  older  empiricists  were  bold  enough — even  in  the  face  of 
the  insuniiountable  difficulty  at  the  third  stage — to  say  that  such 
a  process  of  crystallization  by  the  external  accumulation  of  ideas 
is  the  true  explanation  of  the  thinking  process.  But  the  impossi- 
liility  of  ever  achieving  any  real  continuity  in  this  process  of 
knowing  tilings  together,  led  the  lat(M-  associationists  to  substi- 


■•^  ForvKil  L()()ii\  p.  92. 

'■'Studies  in  Deductive  Loe/ic,  p.   1. 


58  FOOTNOTED  TO  FOBMAL  LOGIC 

tule  analysis  for  synthesis  as  the  central  function  of  thouglit.  On 
this  view  the  most  elemental  judgment — or  if  we  are  not  pre- 
pared to  call  this  primary  state  a  judgment — the  most  primitive 
datum  of  knowledge  is  an  undifferentiated  feeling  or  sensation. 
Judgment  then,  is  not  a  combination  of  two  ideas  into  one,  but  is 
the  separation  of  this  primary  undifferentiated  feeling  into  its 
two  correlated  aspects.  But  this  analytic  process  is  also  embar- 
rassed by  at  least  three  unmanageable  difficulties:  (1)  What 
precisely  is  the  original  feeling,  (2)  what  is  the  principle  of 
differentiation  and  how  does  it  operate,  and  (3)  what  are  the 
two  facts  or  aspects  to  which  the  division  leads? 

The  ancient  dilemma  of  ignava  ratio  which  conceals  the 
fallacy  of  incomplete  disjunction  has  been  perpetuated  in  the 
modern  attack  upon  the  validity  of  judgment.  Predication  is 
discredited  today  in  almost  the  identical  language  of  the 
Sophists.  Eitlier  our  predicate  is  contained  in  the  subject  or  it  is 
not.  If  it  is  not,  we  have  no  right  to  say  that  the  subject  is  the 
predicate,  and  the  judgment  is  false ;  if  the  predicate  is  already 
in  the  subject,  the  judgment  is  idle.  Now  I  submit  that  this 
argument  is  cogent  only  in  the  sphere  of  quantity  where  the  term 
"contained  in"  has  application  in  an  intransitive  relation  only. 
In  the  quantitative  world  an  object  cannot  be  both  inside  and 
outside  of  a  class.  But  the  relation  between  subject  and  predi- 
cate in  judgment  depends  upon  a  totally  different  conception  of 
a  class.  The  two  alternative  positions  in  which  the  predicate  is 
placed  in  the  ancient  dilemma — inside  or  outside  the  .subject — 
do  not  exhaust  the  possibilities.  With  a  ditt'erent  conception  of 
the  relation  of  a  term  to  its  class  the  predicate  may  be  both  inside 
and  outside  of  the  subject ;  there  is  both  novelty  and  identity 
in  judgment — stability  and  risk.  This  very  important  subject 
of  novelty  and  identity  in  judgment  I  propose  to  discuss  farther 
in  a  special  cliapter. 


TiiK  iMJ'oirr  or  .n dcmf.st  59 

TV 

It  will  not  be  necessary  for  the  fi:eMei*al  |)Ui'|)Ose  of  this  inquiry 
into  the  nature  of  jud^nient  to  ^o  into  any  detailed  consideration 
of  the  pei-emiiai  <|uestion  as  to  whether  the  class  rinr  of  predica- 
tion is  logically  fundaineiilal.  1  shall  discuss  the  class  view  of 
predication  and  the  suhjeet  of  the  relation  of  extension  to  inten- 
sion in  considering  the  validity  of  the  syllogism.  I  nnist,  liow- 
evei',  point  out  at  this  time  what  seems  to  be  a  very  prevalent 
mistake  in  the  moi'c  recent  criticisms  of  the  class  i-icw.  Windel- 
band  says : 

As  far  back  as  Aristotle,  Logic  has  givcu  way  to  the  temptation  of 
regarding  the  subject  thus  conceived  as  falling  within  the  sphere  of  the 
predicate  as  the  type  of  all  judgment,  and  subonlination  or  subsumption 
as  the  prevailing  meaning  of  the  copula.  This  is  an  error  in  principle  of 
the  scholastic  logic,  "Gold  is  a  metal,"  is  indeed  a  real  subordination;  but 
' '  Gold  is  yellow ' '  never  means  in  living  thought  that  gold  ought  to  be 
subsumed  under  yellow,  which  would  be  obviously  uonsense — and  certainly 
not  always  that  gold  is  to  be  reckoned  among  yelloAv  bodies,  but  rather  that 
gold  has  the  property  of  yellowness.  Subsumption  may  be  thought  of  as  a 
side  issue,  but   it  is  not  tlu>  precise  meaning  of  the  judgment. lo 

Windelbaml  has  failed,  in  my  opinion,  to  state  the  precise 
grounds  of  the  distinction  between  a  "side  issue"  and  a  "pre- 
cise meaning."  If  these  two  expressions  are  to  be  taken  as 
synonymous  with  ■'essential**  and  "aeeidental,""  then  by  defini- 
tion the  side  issue  or  accidental  charactei'istic  of  judgment 
cannot  be  regarded  as  the  prevailing  meaning  of  the  copula.  Rut 
if  the  side  issue  is  always  an  essential  side  issue,  that  is,  if 
it  is  a  real  i)i-operty  in  the  scholastic  sense,  we  may  for  certain 
l)urposes  consider  it  the  i)recise  meaning  and  relegate  the  former 
pi-eeise  meaning  to  the  position  of  side  issue.  If  the  judgment 
has  various  meanings,  all  e(|ually  present,  by  what  criterion  shall 
we  decide  between  the  primary  and  the  secondary  meaning — the 
precise  meaning  and  the  side  issue.     How  mucli  we  mean  when 


lOEnci/.  Pltilo.s.   Sri..   I,  M. 


60  FOOTNOTES  TO  FOMMAL  LOGIC 

we  say  ' '  all  men  are  mortal, ' '  how  we  reach  these  meanings,  and 
how  we  rank  them  in  importance,  is  the  basic  question  in  Logic. 

Tliis  distinction  between  the  main  issue  and  the  side  issue, 
the  bona  fide  meanings  and  the  spurious  meanings  has  been  car- 
ried into  the  distinction  between  the  problematic  and  the  apo- 
deictie  judgments.  Professor  Sidgwick  has  said:  "No  propo- 
sition can,  after  all,  be  more  than  true;  that  no  piling  up  of 
adverbs  like  'certainly'  or  'necessarily'  will  intimidate  the  actual 
facts.''"  But  the  modal  adverbs,  I  submit,  have  no  intention  to 
"intimidate  the  facts";  they  apply  to  the  thought  about  the 
facts,  not  to  the  facts  themselves.  The  attempt  to  dispense  with 
modality  in  propositions  rests  back  upon  the  denial  of  the 
scholastic  distinctions  between  rationes  cogsnosccndi  and  rationes 
essendi.  The  reasons  for  knowing,  or  perhaps  we  should  say 
the  reasons  for  'belief,  may  vary  from  the  zero  of  pure  doubt 
to  entire  conviction.  The  reasons  for  being  exhibit  no  such 
gradations.  It  is,  indeed,  a  contradiction  in  terms  to  speak  of 
reasons  for  being.  But  there  are,  and  must  be,  reasons  for 
knowing,  and  when  knowledge  searches  for  its  reasons  it  epitom- 
izes these  supporting  or  inferential  judgments  in  modal  adverbs. 
The  necessity  in  apodeictic  judgments  depends  upon  scientific 
or  demonstrative  evidence,  while  the  necessity  in  assertoric  judg- 
ments depends  solely  upon  enumeration  or  observation. 

The  act  of  comparison  which  our  theory  regards  as  the  pri- 
mary function  of  judgment  is  not  so  simple  a  process  as  on  the 
surface  it  appears  to  be.  Comparison  involves  cross-reference  of 
one  object  to  another,  that  is,  each  object  submits  to  being 
assessed  by  a  principle  which  is  inherent  in  the  other  object. 
Bosanquet  thinks  that  comparison  is  not  necessary  to  every  judg- 
ment. Comparison  he  holds  can  not  be  expressed  with  complete 
convenience  in  a  single  judgment.  Now  it  is  true  that  the  com- 
paring act  is  not  evident  in  the  judgment  in  its  simple  form ; 
but  when  the  entire  content  of  the  judgment  becomes  explicit 


11  Elemcntdrij  Loc/ic,  j).  71. 


7  ///•;  iMi'oirr  of  .udomest  6i 

and  it  is  made  fully  aware  of  its  reasons,  tlieii  eoiii[)arison  is  seen 
always  to  lie  at   its  heart. 

Moi-e  is  needed  for  an  aet  of  judj^niciil  llian  just  the  juxta- 
position of  suhjeet  aiid  i)redicate  in  eonseiousness.  ( "oniparison 
means  more  than  simple  association.  Tiie  association  theor}'  of 
thought  is  incapable  of  bridging  the  gap  between  the  two  facts, 
taken  sinij»l\-  as  facts  in  relation.  Tliou^lit  must  betake  itself 
to  tlie  eireumambieid  universal  at  each  step.  However,  tlie 
nnivri-sal  which  is  thus  operative  in  each  particular  state  of 
consciousness  is  not   ahva\s  manifest.     As  Bosanquet  has  said: 

Its  oiK'i-atioii  is  exteiidoil  tliioui^liout  a  scrie.s  of  tlio  fugitive  psyeliieal 
facts  or  ideas,  and  altliough  in  logical  thinking  its  operation  is  conscious, 
i.e.,  selects  and  modifies  within  the  content  of  these  ideas,  yet  it  is  not  in 
itself  necessarily  a  conscious  activity.  It  acts  in  consciousness,  but  need 
not  be  conscious  of  its  own  principle  of  action. 12 

V 

The  teaching  of  ordinary  Logic,  that  every  proposition  is  a 
si-ntence  but  not  every  sentence  is  a  proposition,  is  not  entirely 
free  from  criticism.  It  is  alleged  that  only  the  declarative  sen- 
tences are  true  propositions.  But  everj'  sentence  has  a  mean- 
ing, even  the  imperative,  optative,  and  exclamatory  sentences; 
though  these,  to  ])e  sure,  cannot  be  said  to  be  either  true  or  false, 
in  the  form  in  which  we  find  them  expressed.  The  old  familiar 
definition  of  a  sentence — that  it  is  an  expression  of  thought  in 
words — tells  a  hidden  truth  about  those  forms  which  are  com- 
monly not  admitted  to  the  rank  of  real  projiositions.  A  thought 
is  always  im|)lie(l  in  every  command,  wish,  or  exclamation.  A 
complete  analysis  of  the  states  of  consciousness  corresponding 
to  the  various  so-called  sentences  would  reveal  both  a  cognitive 
and  an  emotional  aspect  in  each.  In  the  indicative  mood  the 
cognitive  chai'actei'istic  is  overt  anil  tlie  emotional  ehai'aeteristic 
is  implied.     In  the  other  moods  the  emotional  aspect  is  exiiressed 

1-  Lo(/i(\  II,  C. 


62  I'OOTNOTEti  TO  FOKMAL  LOGIC 

and  the   judgment,   or   assertion,   or   cognitive   characteristic  is 

implied.     The  exclamation  "fire,"  the  command,  "avaunt,"  the 

ivish    "a   horse!     my   kingdom    for   a   horse,"   each   implies   an 

assertion  which  is  not  expressed.     Instrumental  Logic  is  quite 

right  in  maintaining  that  for  the  purposes  of  complete  definition 

and   in   our   practical   lives   we  should  take   into  account   these 

implications.      I)ut   it   is  wrong,   in   my   opinion,   to  assert   that 

it    is    impossible   to    detach    the    cognitive    factoi-    for    exclusive 

study. 

A  state  of  consciousness  may  be  simi)le  and  unequivocal  while 

its  outward  expression  may  be  duplex,  that  is  to  say,  one  judg- 
ment may  require  for  its  expression  two  propositions.  And  on 
the  other  hand  there  may  be  a  multiple  content  in  mind — two 
or  more  judgments — with  only  one  proposition  to  represent 
them.  Illustrations  of  the  former  we  find  in  the  rhetorical 
devices  for  securing  emphasis  through  tautology,  repetition  or 
elaboration.  "The  last  rose  of  summer  is  gone.  It  is  fled," 
are  two  sentences  or  propositions,  but  one  judgment.  "All  the 
planets  except  Venus  and  Mercury  are  outside  the  earth's  orbit," 
"None  but  the  brave  deserve  the  fair,"  are  duplex  propositions. 
Each  is  in  form  a  single  sentence  containing  two  assertions.  The 
name  exponihle  which  was  given  by  the  older  logicians  to  these 
propositions  with  multiple  meanings  was  etymologically  some- 
what unfortunate.  Any  of  the  more  modern  words  plurative, 
duplex  or  portmanteau  propositions  is  to  be  preferred.  A  care- 
ful analysis  of  these  portmanteau  propositions,  particularly  the 
exclusive  propositions,  which  are  either  omitted  or  given  only 
slight  consideration  in  most  discussions  of  the  import  of  proposi- 
tions will  throw  light  upon  the  nature  of  judgment  and  of  infer- 
ence. In  the  exclusive  proposition  "None  but  the  brave  deserve 
the  fair,"  we  have  the  interesting  situation  of  two  judgments 
and  two  propositions  telescoped  into  one  sentence.  It  is  likewise 
interesting  as  an  illustration  of  an  attempt  on  the  part  of  the 
speaker  to  r(M-ognize  the  existential  import  of  propositions  but 


'/■///•;  iMi'dirr  <if  .ir dcmest  6.'} 

to  pi'ovidc.  ill  llic  t'ofiii  of  till'  assi'i'tion,  foi'  a  lioii-coiniiiittal  atti- 
tude toward  tin'  (iiicstioii  of  the  existcnc'c  of  tlic  subject. 

It  is  often  saiil  that  the  ediieat  ioiiai  \'alue  of  eleineiitary 
Foi'iual  Logic  consists  cliietly  in  tlie  exercise  of  parapln-asiiig 
poetical  oi-  rlietorical  assertions  nito  tlie  type-forms  of  i)roposi- 
tions,  witli  the  least  possible  sacrifice  of  meaning.  I  do  not  think 
this  is  true.  The  translation  of  propositions  from  their  rhetorical 
to  theii-  logical  form  is  a  litei-ary  occupation.  This  is  a  task  that 
l)roperly  lielongs  to  the  graiiimarian  and  the  philologist,  not  to 
the  logician  as  such.  Tliis  is  an  interesting  and  important  woi'k, 
but  it  is  no  more  the  special  business  of  Logic  than  the  transla- 
tion of  a  foreign  language  would  be.  The  franslations  of  propo- 
sitions should  be  distinguished  fi"om  their  transformations.  The 
task  of  tlie  logician  begins  aftei-  the  student  of  language  has 
translated  the  poetic  or  rhetorical  form  into  the  type-proposi- 
tions, lie  has  tlie  task,  then,  of  transforming  the  standardized 
})roposition  into  its  various  implications.  Logic  is  the  science 
of  inference,  not  the  art  of  transhitio)i.  Given  an  unequivocal 
type-form  it  is  the  business  of  the  logician  to  classify  all  the 
other  propositions  that  deal  with  the  same  subject  and  predicate 
as  true,  false  or  doubtful.  And  this  involves  an  intellectual 
discipliiu^  of  great  interest  and  value.  The  recent  successful 
developments  of  Symbolic  Logic  exhibit  moi'e  truly  the  proper 
scope  of  Logic,  than  does  Genetic  or  Instrumental  Logic.  I 
repeat  the  criticism  so  often  made,  that  the  latter  is  not  Logic 
but  Psychology. 

An  excellent  illustration  of  the  failure  to  distingiush  between 
Gi'ammar  and  Logic  is  found  in  Dr.  !Mercier's  treatment  of 
])ropositions.     He  writes: 

For  logical  purposes,  the  most  important  ilistinetion  between  diflfereut 
propositions  is  that  between  the  Incomplete  and  the  Complete.  This  is  a 
distinction  new  to  Logic,  but  it  is  one  of  tlie  greatest  importance.  An 
incomplete  jiropositiou  is,  as  its  title  implies,  a  proposition  of  which  an 
element  is  missing.  Every  proposition  expresses  a  relation ;  and,  as  Ave  shall 
find    further   on,    a    relation    consists   of   three   elements — two    related    terms, 


64  FOOTNOTES  TO  FOBMAL  LOGIC 

and  the  ratio  which  expresses  the  relation  between  them.  Any  one  of  these 
elements  may  be  missing.  ...  In  the  proposition  "A  is  B, "  the  term  A 
may  be  missing;  but  we  can  keep  the  proposition  in  form  until  the  missing 
element  can  be  supplied,  and  at  the  same  time  introduce  a  reminder  that 
the  term  is  missing,  and  needs  to  be  supplied,  by  putting  in  place  of  the 
missing  term  the  relative  ' '  Avhat. ' '  By  this  means  we  obtain  the  incom- 
plete proposition,  "What  is  B. "  Similarly,  if  B  is  missing,  we  can  throw 
the  incomplete  proposition  into  the  form,  "A  is  what?"  These  are  mani- 
festly questions,  and  should  be  characterized  as  questions  by  the  addition 
of  the  interrogation  sign ;  and  we  then  get  the  incomplete  propositions, 
"What  is  B?"  "  A  is  what?"  which  at  once  preserve  the  form  of  the 
proposition,  and  remind  us  that  the  proposition  is  incomplete  and  clamors 
for   completion.!^ 

Here  it  seems  to  me,  Dr.  Mercier  has  disregarded  tlie  vital 
distinction  between  a  question  and  a  proposition.  He  is  quite 
right  in  asserting  that  all  propositions  are  preceded  by  questions 
of  some  sort.  The  question  may,  indeed,  be  most  vague  and 
amount  merely  to  a  psychological  restlessness,  but  this  question 
is  one  thing,  and  the  assertion  that  follows  upon  it  quite  another. 
If  instead  of  writing  these  so-called  propositions  as  a  question, 
for  instance,  "What  is  B?"  he  had  written  it  as  an  assertion, 
"Somewhat  is  B,"  he  would  have  been  closer  to  the  facts  as  we 
find  them  in  the  mind.  These  so-called  incomplete  propositions 
correspond  not  to  incomplete  but  to  indefinite  judgments.  It  is 
not  true  that  there  is  no  subject  but  that  the  nature  of  the  asser- 
tion is  such  that  we  are  not  able  or  not  concerned  to  specify  it. 
The  whole  meaning  of  the  judgment  has  gone  over  into  the 
predicate,  and  in  the  subject  position  we  have  a  that  without  a 
what.  This,  I  believe,  is  the  true  account  of  the  impersonal 
propositions. 


13  Neiv  Logic,  p.  30. 


riiF.  iMi'Ojrr  of  jii>i;.\]j-:.\'J  65 


VI 


Every  judgiiicnt  flaiiiis  to  he  ti'iic;  if  i1  did  not,  it  woidd 
forfeit  its  i-ight  to  he  calii-d  a  jiid^Miiciil .  This  ciaiiii  to  he  true, 
means  tliat  the  iiiiiid  tliat  jiidf^es  distiiif^iiislies  Ix'tweeii  idea  and 
ol)je('t,  ill  r'eeo^in/iiig  tliat  it  might  have  an  idea  which  is  not  in 
agreenK'iit  with  the  object.  Here,  again,  it  is  necessary  to  dis- 
tinguish between  a  judging  consciousness  ami  one  that  merely 
apprehends.  The  difference  between  the  two  is  that  one  con- 
fesses the  possibility  of  error,  while  the  other  knows  nothing 
of  the  distinction  between  truth  and  falsity.  There  is  an  essen- 
tial difference  between  the  simple  appr< lioisioii  "This  is  A," 
and  the  judgnunt,  "This  is  A."  The  judgment  is  never  merely 
the  awareness  of  something  present.  It  asserts  qualities  that 
are  dei'ived  fi'oiii  relations  which  transcend  the  present.  And 
in  this  reference  to  facts  not  present  there  is  the  risk  and  the 
possibility  of  error  which  differentiates  the  judgment  from  the 
apprehension.'* 

Error  is  the  most  perplexing  subject  in  the  whole  field  of 
Philosophy.  Why  does  it  exist?  Or  is  there  perhaps  no  such 
thing  as  ei-ror,  as  the  sophists  alleged?  Plato  felt  called  upon 
to  devote  an  entii'e  dialogue  to  the  refutation  of  the  sophist's 
view  and  after  twenty-three  centuries  the  Jiew  realists  find  it 
their  most  embarrassing  problem.  There  would  truly  never  be 
any  error,  we  should  never  make  mistakes  in  judging,  if  we 
never  took  any  i-isk  in  the  predicate,  if  we  always  said  "A  is  A," 
and  never  attempted  to  predicate  of  .1  something  other  than  its 


!•*  On  tliis  point  see  Sidgwiek,  Elemcntanj  Logic,  p.  196.  "Tliis  risk, 
tlien,  is  always  present  wiien  we  make  a  predicative  statement,  liowever 
carefully  worded  the  statement  may  be.  There  is  no  way  of  escaping  it, 
short  of  ceasiiii;-  to  make  any  predications  at  all.  It  is  the  price  we  pay  for 
the  power  either  of  generalisinij  or  of  descriljin<j  a  Subject;  it  is  a  defect 
that  l)elonf,rs  to  a  quality. ' '  I  slioul.i  a<i;ree  entirely  Avith  this  account  of 
the  essential  risk  in  judgment,  but  should  differ  as  to  its  ixitetpretation.  In 
the  chapter  on  "Novelty  and  Identity  in  Inference"  I  have  tried  to  show 
that  the  risk  in  judgment  is  not  destructive  of  a  stability  t'.tat  is  just  as 
essential  as  the  risk. 


6(i  FOOTXOrES  TO  FOBMAL  LOGIC 

bare  identical  self,  something  genuinely^  different  from  it.  Hut 
we  do  take  the  risk  and  must  take  it.  And  it  is  the  business 
of  critical  philosoi)hy  to  ask  for  the  reason  why  we  take  tlie 
risk  and  what  is  the  success  of  our  venture.  We  see  at  once, 
that  the  modern  query,  "How  can  one  mind  contain  both  the 
possibility  of  knowledge  and  the  liability  to  error?"  is  identical 
with  Kant's  fundamental  problem,  "How  are  synthetic  judg- 
ments a  priori  possible?"  and  this  in  turn  is  the  same  as  Plato's 
question,  "How  can  we  affirm  of  a  subject  a  non-identical 
predicate  ? " ' 

It  is  very  easy  to  state  the  difficulties  about  error,  but  far 
from  easy  to  remove  them.  The  Law  of  Excluded  Middle 
declares  that  reality  and  non-reality  exhaust  the  entire  universe. 
Now  from  the  purely  subjective  point  of  view,  that  is,  before  we 
attempt  to  classify  any  of  the  facts  of  universe,  this  law  is  com- 
pelling. A  thing  is  either  real  or  it  is  not  real ;  we  cannot  accept 
anything  between  these  two.  When,  however,  we  begin  the 
process  of  classifying  subjective  and  objective  facts,  on  this 
principle,  we  get  along  very  well  until  we  come  to  the  group  of 
negative  conceptions  among  which  error  is  found.  These  stub- 
bornly refuse  to  go  into  either  of  the  two  aforesaid  classes. 
Error,  for  instance,  refuses  to  be  classed  as  either  reality  or 
non-reality.  It  insists  upon  having  a  third  place  made  for  it. 
for  wliich  as  we  have  just  seen.  Logic  at  the  outset  makes  no 
provision.  There  is  truth  in  the  remark  that  error  is  the  occu- 
pation by  an  actuality  of  a  place  which  does  not  exist. 

Thus  does  thought  discover  a  most  interesting  dilemma  about 
thought.  It  can  compel  truth  to  reveal  its  own  intrinsic  false- 
hood. Also  it  can  extract  from  error  the  confession  of  its  essen- 
tial reality  and  necessity.  To  i)ut  it  otherwise,  in  the  manner 
of  Bradley,  an  appearance  which  is,  must  fall  somewhere.  But 
error,  because  of  its  intrinsic  negativity  cannot  belong  to  reality, 
and  again,  it  cannot  l)elong  to  appearance,  because  that,  with  all 
its  contents,  cannot  fall  outside  the  Absolute.     An  appearance 


'////■.  I. \i  I'd  in  OF  .11  iicM  i-:sT 


07 


I'litii'fly  outside  of  l{c;ility  is  luiiij^lit .  Tlie  I'ssi'iitial  ciiaractcr- 
istie  of  falsehood,  ei-i-oi-.  lietion,  is  lliat  an  ae1iialit_\-  slioidd  claim 
to  he  soiiiet  hiiiu'  otliei'  than  itself.  Aiaii.\'  of  the  |)0|)idai'  wit- 
ticisms are  hased  on  liiis  fuiidameidai  j)ai-a(h)x.  h'oi'  example, 
the  (h'fiiiitioM  of  a  liar  as  one  who  tells  the  tnitli  ahout  something 
that  iie\ei-  happened.  It  will  he  ohsei'xed  that  I  have  <litfercd 
from  l>r;idley  as  to  the  jdace  of  efi-or  in  juduiiient .  He  con- 
tends'"' that  we  can  not,  while  makinji:  a  .iud):;!:meiit  entectain  the 
possihility  of  its  efi-oj-.  One  can  not  judge  and  douht  at  the 
same  timi'.  1  Iuinc  insisted  that  one  does  not  judge  unless  one 
does  feel  the  actual  const  i-aint   of  a  douht. 


■^■'Miiul,  n.  s.  XVir   (1908),  1.14. 


CHAPTER   IV 
NEGATION  AND  THE   INFINITE  JUDGMENT 

I 

There  are  four  possible  ways  in  wliich  we  may  regard  the 
relation  between  the  affirmative  and  the  negative  judgment.  We 
may  hold  that :  ( 1 )  each  is  an  independent  and  final  form  of 
thought's  functioning — original,  underived  and  self-directing; 
(2)  negation  comes  after  affirmation  and  is  the  result  of  a 
thwarted  affirmation;  (3)  affirmation  follows  negation  and  is 
what  we  find  left  over  after  negation  has  destroyed  certain 
possibilities;  (4)  affirmation  and  negation  are  correlated  aspects 
of  a  more  fundamental  form  of  thought. 

Tlie  first  is  the  view  of  common  sense  and  need  hardly  be 
discussed,  although  it  is  the  innocent  presupposition  of  some 
systems  of  Logic.  It  has  been  included  in  this  fourfold  classi- 
fication for  the  sake  of  formal  completeness.  The  second  view, 
which  makes  negation  subordinate  to  affirmation,  has  had  many 
advocates,  notably  Sigwart  and  Erdman.  The  third  doctrine, 
omnis  dcierminatio  est  negatio  has  had  able  defender^  from 
Spinoza  to  Venn.  Although  this  controversy  concerning  the 
logical  priority  is  many  centuries  old,  the  supporters  of  the 
second  and  the  third  views  are  still  quite  equally  divided,  which 
suggests  that  each  side  has  hold  of  one  aspect  of  a  multiple  truth. 
The  fourth  position  maintains  that  neither  affirmation  nor  nega- 
tion is  logically  prior,  and  that  while  each  necessarily  involves 
the  other,  both  are  dependent  upon  a  more  central  form  of 
thought.  This  view  makes  possible,  it  seems  to  me,  a  genuine 
reconciliation  of  the  divergent  claims  of  (2)  and  (3). 

Sigwart 's  view  that  every  negation  presupposes  an  affirm- 
ation,   has   been   characterized   as   "monstrous"   by   Bosanquet. 

[68] 


SKliATIOS  AM)  TIN-:  IS Fl SITE  .11  DCMEST  tJ9 

However,  we  must  admit  this  is  a  true  and  accurate  description 
of  a  stage  in  tlie  complex  wliole  of  the  judging  jjrocess.  That 
reality  is  a  system  of  inter-related  facts  is  a  postulate  of  every 
judgment.  This  affirmation  of  an  orderly  whole  which  is  the 
logical  presupposition  of  every  specific  judgment,  always  takes 
the  form  of  a  disjunctive  judgment.  It  is  an  assertion  to  the 
effect  that  reality  offers  alternative  possibilities  to  the  judging 
consciousness.  "^  is  either  P  or  )ion-T\"  Bosanquet'  and 
Bradley-  are  doubtless  right,  however,  in  saying  that  this  postu- 
late can  not  properly  be  called  an  affirmative  judgment.  Judg- 
ment implies  belief  and  we  can  liardly  l)c  said  to  liavc  judged 
and  "believed"  when  the  iniiid  is  ])ois('d  between  tlie  balanced 
terms  of  a  disjunction. 

This  postulate,  or  disjunctive  affirmation,  which  precedes 
the  negation  is  not  the  same  in  kind  as  the  affirmation  which 
comes  after  the  negation.  They  differ  as  suggestion  differs  from 
assertion.  It  is  true  that  in  the  life  history  of  the  judging 
process  negation  does  occur  between  two  affirmative  states.  But 
the  one  is  an  ideal  construction  and  the  other  an  affirmation  of 
fact.  The  prior  disjunctive  judgment  is  a  crucial  instance, 
and  has  the  same  structure  as  a  genuine  hypothesis  in  science. 
It  is  strictly  non-committal.  Tt  has  been  said  that  the  suggestion 
in  the  disjunctive  judgment  is  the  same  as  the  assertion  that 
I'cmains  after  tlie  selective  process  of  negation.  This  is  the  only 
view  that  lends  supi)ort  to  Sigwart's  doctrine,  but  this  is  clearly 
untenable.  We  can  not  say,  as  Sigwart's  view  would  have  us 
say,  that  negation  is  the  rejection  of  an  actual  judgment.  The 
acce])tance  of  the  bare  presentation  of  the  choice  between  alter- 
native possibilities  is  not  a  judgment. 

Bosanquet  says,  "Every  significant  negation,  S  is  not  P  can 
be  analysed  as  S  is  X  which  excludes  P."  But  now  we  may 
properly  a.sk  "At  what  stage  has  the  exclusion  taken  place?" 


^  Logic,  I,  321. 

-  Priiiciphs  of  Logic  (Loiulon,  Paul,  1883),  p.  110. 


70  FOOTNOTES  TO  FOEMAL  LOGIC 

If  there  is  no  necessity  for  putting  the  verb  is  and  excludes  in 
the  same  tense,  we  may  consider  the  exclusion  to  have  been  per- 
formed first  and  thereafter  the  discovery  made  that  the  inclu- 
sion of  A  in  X  had  been  atfected  thereby.  The  complex  judg- 
ment would  then  read  as  follows:  A  {B  having  been  excluded) 
is  found  to  be  A'.  This  obviously  would  be  a  return  to  Venn's 
Theory  of  Judgment.  Again  we  might  stress  the  inclusion  and 
say:  A  (in  being  A')  has  excluded  B.  The  vital  question  is 
whether  the  exclusion  is  before,  after  or  simultaneous  with  the 
inclusion?  The  logical  analysis  of  the  content  of  consciousness 
does  give  support  to  the  view  that  the  only  meaning  of  any 
affirmation  of  a  proposition  is  found  in  what  it  denies.  Actuali- 
ties can  not  be  asserted,  they  arise  spontaneously  out  of,  or  by 
the  side  of,  the  destroyed  possibilities.  The  actualities  we  seem 
to  get  by  the  way  of  pure  affirmation  are  always  pseudo-actuali- 
ties; they  have  never  more  than  a  hypothetical  existence.  And 
yet  on  the  other  hand,  the  psycJwlogical  analysis  always  finds 
negation  at  a  point  farther  from  reality  than  affirmation. 

The  logical  negative  does  in  fact  always  contradict,  but  in 
contradicting  never  alfirms  the  reality  of  that  which  has  been 
denied.  The  dichotomy  which  is  at  the  bottom  of  every  nega- 
tion, begins  with  existential  reality,  but  in  breaking  up  the 
whole  into  parts  it  is  powerless  to  keep  in  each  part  the  full 
measure  of  the  reality  of  the  whole.'  The  assertion  that  "S  is 
not  P"  is  the  same  as  the  denial  that  <8  is  P,  and  both  are  equi- 
valent to  "S  is  P  is  false."  And  in  no  one  of  these  three 
equivalent  statements  has  thought  passed  beyond  P  into  non-P. 
No  assertion  is  made  about  the  reality  or  the  non-reality  of  P. 
Bradley  has  maintained  that  negation  can  not  in  any  way  be 
derived  from  affirmation,  nor  affirmation  from  negation,  and  yet 
he  thinks  it  wrong  to  consider  them  coordinate  species  of  a 
higher  form.  But  although  he  is  unwilling  to  accord  to  either 
the  prior  position  in  Logic,  in  Psychology  he  places  negation 


Cf.  Bradley,  Principles  of  Logic,  p.  118. 


SKdATIOS  AM)  rilF.  I S F I S IT i:  .1 IDCMKNT  71 

at'tt'i'  al'linuation.  Siucf  ii('y:alion  jji-i'supposes  a  positive  f^roiuid, 
he  says,  "it  stands  at  a  diffiTcnt  level  of  reflection."  And  this 
a^ain  is  in  aceoi-d  with  llic  view  fxpi'csscd  cai'liri-.  Xo  difficulty 
is  found  when  we  ol)serve  the  distinction  between  tlie  lotjieal  and 
the  i)syeli()lo<.,deal  aspects  of  judgment. 

When  Kradh'V  says  "Nothing  in  the  woi'ld  can  lie  denied 
except  on  tlie  strength  of  positive  knowledge,"  lie  is  after  all 
admitting  the  main  contention  of  those  who  hold  that  negation  is 
a  tliwarted  affii-mation.  It  is  true,  as  has  already  been  sliown, 
that  llie  prior  aflii'iiiat  ion  which  he  concedes  does  not  rcfei'  the 
ide.d  content  to  I'eality  with  the  same  claim  to  tr-uth  ;is  ihe 
iatei'  aftirmation,  namel\',  that  whicii  selects  from  among  the 
presented  alternatives.  Tlie  Hist  is  a  siiggrsted  affirmation  while 
the  second  is  an  (iss(r(<(l  affirmation.  Uut  Sigwart  himself 
recognizes  the  essential  ditfei'ence  between  tliese  two  forms  of 
affirnuition  wlien  he  says,  "The  primitive  judgment  should  not 
be  called  affirmative  at  all ;  it  would  be  better  denoted  as  positive. 
The  simple  statement  A  is  B  is  an  affirmation  onl.x-  when  opposed 
to  the  negative  judgment."  In  view  of  this  exjjlicit  statement 
I  do  not  see  why  Bradley  finds  Sigwart 's  doctrine  so  "obviou.sly 
al)surd." 

There  is  a  prevalent  tendency,  especially  in  the  elementary 
textbooks  of  Logic,  to  define  affirmation  and  negation  in  terms 
of  ai)proval  and  disappi'oval.  This  is  not  i)recisely  accurate,  for 
there  is  also  an  asjx-ct  of  approv;il  hiteiit  in  every  negation.  We 
accept  negation  as  true  or  false,  and  thus  approve  or  dis- 
approve* It  is  impossible  in  thought  to  draw  a  line  between 
affirmation  and  approval.  We  do  not  first  affirm,  and  then,  after 
having  contemplate(l  the  object  of  our  affirmation,  pass  to  a 
second  act  of  approval.  Ajiin-oval  and  affii'iiiation  are  sinud- 
taneous.  In  discussing  the  relation  between  ai)prehension  and 
judgment,  we  saw  reason  to  distinguish  between  mere  acknowl- 


■»  On  this  point  see  Sigwart,  Loi/ic;  translatfij  hv   Dcmlv  (ed.  2;  London, 
Macniillan,   1895),  I,  •^8\. 


72  FOOTNOTES  TO  FOBMAL  LOGIC 

edgment  of  a  content  without  critical  reaction,  and  true  judg- 
ment or  acceptance  through  criticism.  But  this  we  held  was  a 
theoretical  distinction  entirely.  In  living  thought  there  is  a 
simultaneity  in  the  midst  of  the  succession. 

II 

The  infinite  judgment  has  been  much  discredited.  Since  it 
attaches  no  positive  and  definite  characteristic  to  the  subject, 
it  has  been  condemned  as  idle,  practically  worthless,  and  even 
illogical.  Honesty  is  non-blue,  for  instance,  is  meaningless, 
because  the  negative  term  includes  all  possible  predicates  other 
than  blue  and  does  not  even  so  much  as  insif^t  upon  the  existence 
of  the  predicate.  It  is  the  farthest  limit  of  indifference.  This 
doctrine  of  the  essential  irrationality  and  futility  of  the  infinite 
judgment  is  very  old.  By  some  it  has  been  traced  back  beyond 
Plato  to  Anaximander.  But  I  must  point  out  at  once,  as  bear- 
Plato  to  Anaximander.  But  I  must  point  out  at  once,  as  bear- 
ing upon  a  later  defense  of  the  infinite  judgment,  that  the  aireipov 
of  Anaximander  was  a  positive  infinite,  and  by  him  regarded 
as  the  source  or  original  of  all  things.  ^Modern  writers  think 
they  find  justification  for  the  contempt  which  they  heap 
upon  the  infinite  judgment  in  Aristotle's  own  treatment  of 
the  subject.  But  we  may  doubt  whether  Aristotle  would  have 
approved  of  this  later-day  entire  condemnation  of  the  infinite 
judgment.  This  problem  first  presented  itself  to  Aristotle  in 
his  discussion  of  terms.  He  saw  as  plainly  as  any  one  since  his 
time  that  there  is  a  paradox  about  the  negative  term.  It  must 
be  defined  as  a  terra  which  implies  the  total  absence  of  a 
quality.  Technically  speaking  it  connotes  the  absence  of  conno- 
tation. It  is  the  self-contradictory  attempt  to  make  something 
out  of  nothing.-'^ 


3  Bosanquet  has  stated  the  dilemma  with  admirable  clearness:  "The 
Negative  Judgment  presents  at  first  sight  a  paradoxical  aspect.  We  are 
bound  to  take'  it,  qua  judgment,  as  playing  some  part  in  knowledge,  and 


XKGATIOX  AM)  Till-:  I S F I S IT E  .11  DCMEST  7.". 

It  is  allfg«'(l  to  \k'  a  st'lt'-c.onti'adicttioii  to  say  tliat  a  t<*nii  may 
connote  just  the  absence  of  a  (|uality.  It  is  not  strictly  speak- 
in<j:  ti'iic,  wt'  ai'c  toM,  as  is  ot'lm  sii|»i)osi'(l  by  the  opponents  of 
bare  denial,  that  no  term  can  be  purely  nej^ative.  But  now  it 
depends  entirely  on  what  we  mean  by.  a  purely  negative  term. 
The  class  of  privative  terms,  which  logic  has  been  compelled  to 
recognize  from  the  first,  is  a  genuine  class;  and  the  definition  of 
this  class  of  terms  must  be  greatly  straini'd  to  allow  even  a 
modicum  of  ])ositiv('  (|uality  in  a  privative  tei-m,  in  the  ordinai-y 
interpretation  of  the  word  positive.  A  positive  character  of  an 
entirely  different  sort  it  does  possess.  The  negative  term  denotes 
an  object  which  in  the  first  place  lacks  the  qualities  denied  by  the 
negative  term  but  has  other  ((ualities  in  terms  of  which  that 
very  lack  is  defined.  Evci-y  negative  must  luive  a  i)ositive  basis. 
A  sheer  naught  can  not  be  the  ground  of  a  denial.  Non-P  will 
always  signify  what  an  object  will  be,  which  might  be  P,  but  is 
not.  But  granted  that  these  so-called  privative  terms  do  have 
a  genuine  positive  connotation,  even  if  sliglit,  there  seem  to  be, 
nevertheless,  other  terms  which  have  no  pui-posc  other  than  to 
deny.  An  alien,  even  within  a  limited  universe  of  discourse,  is 
defined  entirely  in  terms  of  what  he  is  not.  A  bachelor  connotes 
an  unmarried  man,  and  bachelors  (as  bachelors)  have  nothing 
in  common  save  that  they  are  not  married.  Such  terms  are 
positive  as  to  denotation,  but  negative  as  to  connotation.  But 
even  these  terms  can,  I  believe,  be  brought  under  our  general 
rule.  The  i)Ositive  term  as  understood  by  common  sense  and 
ordinary  logic  is  positive  directly  and  definitely,  the  negative 
term  is  positive  indirectly  and  indefinitely,  but  none  the  less 
genuinely.     In  a  latei-  ehajjter  on  immediate  inference  I  shall 


as  at  any  rate  capable  of  contributiiio;  some  factor  to  the  ideal  fabric  of 
reality.  But  it  assumes  the  external  shape  of  ignorance,  or  at  least  of 
failure,  and  the  para<lox  consists  of  this — that  in  negation  the  work  of 
positive  knowledge  appears  to  be  performed  by  ignorance.  The  contradic- 
tion arises,  as  we  have  seen  other  contradictions  arise,  from  the  adoption  by 
thought  of  a  shape  which  at  best  expresses  it  but  partially,  ami  the  reten- 
tion of  that  shape  when  the  as|)ect  whi(h  it  diil  express  has  come  to 
be  dwarfed  by  other  aspects  of  knowledge."  Logic,  I,  2!13. 


74  FOOTNOTED.   TO  FOBMAL  LOGIC 

advance  a  new  interpretation  of  the  ancient  rule  for  distribu- 
tion based  upon  this  distinction  which  I  think  answers  the  much 
debated  question  as  to  the  validity  of  inversion. 

We  here  encounter  the  same  problem  that  confronts  one 
wherever  one  has  to  do  with  the  "relational  way"  of  thinking. 
We  begin  with  what  appears  a  mere  couple,  a  two  in  relation. 
But  the  "endless  fission"  breaks  out  and  we  discover  that  no 
relation  is  purely  diadic.  Relations  are  always  within  as  well  as 
hetivefM;  and  while  they  are  explicitly  diadic  they  are  implicitly 
triadic.  In  earlier  paragraphs  we  saw  this  to  be  true  of  the 
relation  between  form  and  matter,  denotation  and  connotation, 
intension  and  extension.  They  are  all  correlatives  having  inde- 
pendent variability  within  some  larger  whole.  Now  this  con- 
ception of  the  essential  triadic  character  of  every  relation  pro- 
vides an  explanation,  I  believe,  for  the  class  of  bare  denials 
which  the  relation  of  affirmation  to  denial  requires.  Every 
object  denotes  a  tJris  or  a  that,  and  connotes  thisncss  and  tliat- 
ncss.  Now  when  a  this  goes  beyond  itself  for  its  connotation 
and  accepts  that  it  ess  for  its  meaning,  we  have — stated  most 
abstractly — a  pure  negation,  a  bare  denial.  And  such  abstract 
statement  of  the  problem  I  venture  to  think  is  not  a  mental 
"fiction."  We  have  thus  properly  provided  for  the  outstand- 
ing "rare"  cases  where  the  mind  halts  between  denial  and 
affirmation. 

All  of  this  suggests,  as  Windelband  and  Kant  before  him, 
have  held,  that  there  is  a  third  kind  of  quality  between  affirma- 
tion and  negation,  and  in  a  sense  coordinate  with  them.  Where 
there  is  no  sufficient  positive  ground  for  a  direct  assertion  the 
mind  is  satisfied  with  probable,  indirect  or  negative  grounds. 
But,  furthermore,  it  should  be  pointed  out  that  every  indictment 
of  the  infinite  judgment,  which  begins,  as  most  criticisms  do, 
with  a  condemnation  of  the  negative  term,  is  an  illogical  pro- 
cedure, for  terms  are  not  the  prior  units  out  of  which  the  judg- 
ment is  constructed.     The  judgment  is  itself  the  unit  of  thought 


NKCATIOX  AM)  TIN':  I S F I S I Tl-:  .inxiMKXT  17) 

and  tlic  negative  tmn  is  di  ri\i-(|  1)_\-  al)st  i  aci  ion.  uv  disiiKMubci'- 
ment  of  a  ptior  infinite,  oi"  limitative  judgment.  We  do  not  find 
the  non-S's  and  the  iii>)t-I''s  lying  about  i-eady  made  and  then 
proceed  to  affii-mations  Of  denials  about  them.  These  negative 
terms  are  the  by-products  of  the  reverse  process.  We  first 
observe  that  P  cannot  be  attributed  to  .S'  and  state  this  fact  in 
the  negative  judgment  "S  is  not  /''."  Whereupon  the  query 
arises,  if  P  can  not  l)e  atti'ibuted  to  .S'.  what  can  be?  In  answer 
to  this  question,  iiou-I'  is  ei'catcil  and  llic  response  is  em])odied 
in  the  pseudo-affirmative  judgment  "<S'  is  non-P."  The  nega- 
tive judgment  ''»S'  is  nnn-P"  affirms  something  indefinite.  There 
is,  therefore,  abundant  reason  to  assert  with  Lotze  that  the  true 
meaning  of  this  latler  judgment  is  nevei-  available  for  practical 
purposes  until  it  is  restored  to  the  negative  which  was  it  source. 
But  now  it  should  be  observed  that  the  negative  term  non-P 
is  not  truly  indefinite  in  the  sense  of  being  wholly  undefine<l  or 
unbounded.  In  the  technical  language  of  the  schoolman,  it  is 
always  distributed.  And  if  it  is  genuinely  distributed  we  do 
have  some  knowledge  that  extends  over  the  entire  class  or  else 
the  ancient  doctrine  of  distribution  I'alis  to  the  ground.  To  say 
that  non-P  is  distributed  is  to  declare  emphatically  that  it  is 
not  entirely  impossible  to  hold  together  the  large  and  apparently 
chaotic  group  of  objects  comprised  in  non-P.  The  fact  of  dis- 
tribution declares  that  there  is  at  bottom  an  essential  homo- 
geneity in  the  grouj).  and  this  guarantees  the  accuracy  of  all 
the  trausfornuitions  in  which  the  negative  term  is  employed 
in  the  vai'ious  immediate  inferences.  Obversion,  or  infinita- 
tion,  is  for  this  reason  a  valid  inference.  I  think  no  defender  of 
the  infinite  judgment  has  ever  claimed  that  non-P  can  exist  as 
an  independent  concept.  We  can  not,  it  is  true,  conceive  such 
a  class  of  objects,  that  is,  we  can  foi-m  no  mental  i)icture  of  it. 
It  is,  therefore,  unin((Ui(jihh  .  but  not  on  that  account  unthink- 
oblf.  We  can  employ  it  both  in  the  theori'tieal  and  in  practical 
thought   processes.     The  symbolic   logician   nuikes  rigorous  use 


76  FOOTNOTES  TO  FOEMAL  LOGIC 

of  it  in  his  theoretical  thinking,  and  the  empirical  scientist 
applies  it  continually  in  his  search  for  causal  connections.  The 
scientist  narrows  the  field  in  any  inquiry  by  destroying,  one  by 
one,  the  possibilities  of  his  multiple  liypothesis.  And,  as  I  have 
already  insisted,  each  destruction  of  a  possibility  is  a  positive 
advance  towards  his  goal. 

It  is  quite  true  that  the  mind  is  rarely  ever  satisfied  to  remain 
in  the  stage  of  bare  denial.  But  it  is  precisely  these  exceptional 
cases  where  it  does  halt  at  bare  denial,  however  rare  they  may 
be,  that  logic  must  take  into  account.  We  may  ask  two  questions 
here:  (1)  Should  we  at  any  time  be  unable  to  pass  through 
bare  denial  to  denial  with  affirmation,  have  we  made  no  logical 
advance  whatever?  (2)  If  the  infinite  judgment  is  illogical 
and  impractical,  how  can  we  explain  its  persistence  in  thought 
and  language?  I  shall  attempt  to  show  that  it  is  no  answer 
to  these  questions  to  say  with  Hegel  that  the  infinite  judgment 
is  "idiotic." 

The  history  of  Logic  has  repeatedly  taken  cognizance  of  this 
dilemma  about  negation,  and  yet,  in  my  opinion,  there  is  no 
real  warrant  for  the  disparagement  of  the  infinite  judgment. 
The  modern  critics  provide  the  answer  to  their  criticisms  in 
the  emphasis  that  they  place  upon  the  difference  between  the 
assertion  of  impossibility  and  the  denial  of  necessity.  Absence 
of  a  reason  for  assertion,  it  is  justly  held,  does  not  mean  the 
presence  of  a  reason  for  denial.  To  have  no  opinion  against,  is 
not  the  same  as  to  have  an  opinion  for.  It  is  possible,  is  not  a 
legitimate  inference  from  we  do  not  know  it  to  he  impossihle. 
There  is  some  justification  for  the  view  that  there  is  no  middle 
ground  between  affirmatioii  and  denial — that  there  is  no  such 
thing  as  suspended  affirmation.  But  now  whatever  position  we 
take  on  logical  the  problems  here  in  question,  it  is  nevertheless 
an  undeniable  psychological  fact  that  the  mind  may  put  itself 
in  three  diffrrent — even  if  not  correlated — attitudes  towards  any 
suggestion.    It  may  not  only  accept  or  reject,  it  may  also  doubt. 


XEGATIOX  .LSI)  TIIE  I S F I S IT K  .11  I)i: M EXT  11 

At  an  clcc'tion  the  coiiiiti'i'  I'ccords  the  "ayc^s"  and  "'noi-.s"  and 
also  llir  "not  voting."  And  in  I'syclioloj^y  we  arc  told  often 
of  the  indirt'erent  zone  tliat  lies  between  tiie  extremes  in  sensa- 
tion. It  is  an  answer  not  to  the  point  to  say  that  the  state  of 
eonseioiisness  called  indecision  is  decision  not  to  decide.  Tiie 
question  is,  Why  do  we  i'e(|uire  for  i'syehoiojjfy  and  practical 
life  a  threefold  division  and  for  Logic  a  twofold  ilivision  ? 

We  see,  therefore,  that  a  careful  examination  of  these  con- 
siderations which  seem  to  militate  against  the  infinite  judgment 
shows  that  they  are  unrounded.  In  the  first  place  it  can  be 
shown  that  the  infinite  judgment,  in  the  process  of  delimiting 
any  univer.se  of  discourse,  if  not  tlie  whole  objective  system,  has 
nuidf  a  distinct  foi-ward  movement.  x\nd  this  step  does  not  have 
to  be  retraced,  that  is  to  say,  a  second  infinite  judgment  in  the 
next  stage  of  division  proceeds  from  where  the  first  left  off.  It 
is  not  like  the  process  of  throwing  a  die  where  each  throw  is 
no  nearer  certainty  than  the  one  before  it.  The  infinite  judg- 
ment is  no  logical  treadmill.  Tn  theory  it  is  true,  as  Plato  and 
after  him  Kant  said,  that  the  infinite  judgment  subtracts  one 
from  the  infinite  number  of  possibilities,  and  leaves  remaining  an 
infinite  number.  But  in  jji'actice,  the  application  of  successive 
infinite  judgnu'uts  does  very  rapidly  reduce  the  total  sphere. 
Only  half  a  dozen  steps  are  needed  in  the  Tree  of  Porphyry 
to  pass  from  a  sumtnum  genus  to  a  very  definite  infima  species. 
A  practical  illustration  of  the  rapidity  with  which  the  successive 
infinite  judgments  will  narrow  a  field  of  inquiry  is  found  in 
the  familiar  pai'lor  game  of  "twenty  questions."  Here  one 
person  undertakes  to  perform  the  apparently  impossible  feat 
of  telling  what  another  is  thinking  about  by  asking  him  twenty 
questions  to  be  answered  only  by  yes  or  no.  This  is  often 
accomplished  with  surprising  swiftness. 

All  the  so-called  negative  results  in  the  experimental  work 
of  scientific  laboratories  may  be  expressed  in  each  instance  in 
the  form  of  an  infinite  judgment ;  and  these  negative  results  are 


78  FOOTNOTES  TO  FORMAL  LOGIC 

surely  not  without  value.  The  scientist  assumes  that  the  object 
of  his  search  will  be  found  in  a  certain  tield,  but  after  laborious 
investigation  discovers  that  he  has  set  up  a  false  hypothesis,  and 
must  seek  elsewhere  for  the  cause  of  the  phenomenon  under 
investigation.  He  registers  this  fact  in  the  infinite  judgment, 
^'S  is  non-P."  And  he  intends  that  the  judgment  shall  be 
genuinely  aiftrmative,  for  he  knows  that  the  phenomenon  must 
have  a  cause.  The  clearing  of  the  field  by  the  destruction  of 
false  hypothesis  is  not  idle.  The  scientist  never  hesitates  to 
publish  his  ' '  failures  to  find ' '  for  the  guidance  of  fellow  workers 
in  the  same  field.  A  negative  Baedecker  (if  one  dared  to  print 
such  a  guide  book)  which  told  tourists  where  not  to  go,  might 
be  more  useful  than  the  positive  form.  It  would  permit  of  real 
discoveries  by  the  independent  seeker. 

ill 

The  symbolic  logicians  have  pointed  out  the  significant  fact, 
that  the  term  P  is  no  more  indefinite  than  the  term  non-P.  Why 
should  we  think  that  the  objects  that  compose  the  class  P  are 
any  more  homogeneous  than  those  of  the  class  non-P?  The 
belief  that  one  of  these  classes  is  small  and  homogeneous  and 
the  other  large  and  heterogeneous  is  an  idea  that  is  thrust  in 
from  without.  Granted  that  the  members  of  the  class  non-P 
have  nothing  in  common  save  the  absence  of  S,  this  does  not 
make  them  a  less  coherent  group  than  the  class  P.  Non-P  is, 
indeed,  the  contradictory  or  negative  of  P,  but  in  Formal  Logic 
either  of  the  two  terms  which  stand  in  the  relation  of  contra- 
dictories may  be  taken  as  the  positive  and  the  other  as  the  nega- 
tive. For  example,  a  powerful  social,  political  or  religious  move- 
ment often  grows  from  small  beginnings  when  its  adherents  were 
described  by  some  negative  word.  The  Anti-Saloon  party  in  some 
prohibition  communities  is  overwhelmingly  large,  positive  and 
coherent.  The  fundamental  fact  with  which  Formal  Logic  is  con- 
cerned is  that  the  two  classes  P  and  non-P  are  mutually  exclusive 
and  together  comprise  the  whole  universe  of  thinkable  entities. 


NEGATION  AND  TIIK  IS  F I  SITE  .IIDCMENT  79 

Symbolic  loj^iciaiis  liavc  also  said  that  Kant's  threefold 
classification  of  propositions  into  positive,  negative  and  infinite 
has  no  theorelic  drffiisc ;  il  (Icpciids  eiilii-cly  upon  practical 
differences  of  meaning.  The  three  foi'iiis  "N  is  P,"  "S  is  not 
/-*/'  and  S  is  non-P  have  their  origin  not  in  aii\'  strict  doctrine 
of  negation,  hut  in  the  practical  convention  of  something  less 
than  coniplt'lc  negation,  namely,  opposition.  In  all  those  jndg- 
ments  in  which  the  predicate  is  regarded  as  an  attribute,  it  is 
for  ])ractical  i)ur])0ses  quite  sufficient  to  use  opposites.  that  is, 
terms  which  iiiutuall\'  exclude  each  other,  as  do  eontradictoi'ies, 
but  which  do  not  together  include  the  entire  universe  of  think- 
able objects.  The  class  of  infinite  judgments  is  a  concession  to 
contrary  negation,  and  to  the  attributive  view  of  predication. 
And  tins  view,  as  I  have  already  tried  to  show,  is  merely  a  neces- 
sary stage  on  the  way  to  the  class  view  of  Symbolic  Logic. 

It  has  often  been  maintained  that  the  assertion  of  a  mere 
distinction,  that  is,  an  assertion  of  differences  in  degree  is  no 
assertion.  This  is  only  partly  true.  The  common  definition  of 
negative  or  contradictory  tei"ms,  that  they  are  two  terms  that 
are  mutually  exclusive  and  that  together  exhaust  the  entire 
universe  of  thinkable  things,  needs  some  qualification.  They  are 
totally  different,  the  definition  says,  that  is,  different  in  kind. 
Now  this  distinction  between  differences  in  degree  and  differ- 
ences in  kind  is  one  which  Logic  has  always  regarded  as  of  the 
deepest  significance.  But  what,  we  may  ask,  is  the  criterion 
of  this  distinction  between  the  differences  in  degree  and  the 
differences  in  kind  ?  Entities  which  are  different  in  kind  must 
after  all  have  something  in  common.  They  must  belong  to  the 
same  universe  of  thought  somewhere,  otherwise  they  would  have 
ceased  to  be  two  and  would  have  become  nothing.  The  Hegelian 
criticism  of  the  Aristotelian  Law  of  Contradiction  is  just. 
Where  there  is  a  distinction  there  must  l)e  at  least  one  principle 
of  unification.  Only  one  thing  can  both  he  and  not  be,  namely, 
nothing. 


80  FOOTNOTES  TO  FOBMAL  LOGIC 

While  A  and  non-A  are  different  in  kind,  yet  it  is  evident 
that  that  which  differentiates  one  of  these  conceptions  from  the 
other  is  not  an  intrinsic  principle.  There  is  nothing  in  the 
nature  of  the  two  conceptions  which  can  tell  us  where  the  one 
ends  and  the  other  begins.  The  principle  of  this  division  is 
alwaj^s  extrinsic,  that  is,  it  lies  in  the  purpose  of  the  thinker. 
Every  dichotomous  division  is  made  in  the  interest  of  an  external 
need.  "Without  such  an  extrinsic  point  of  departure  we  should 
pass  from  A  to  non-A  by  imperceptible  gradations  within  the 
same  qualitative  sphere.  However  far  apart  we  place  A  and 
non-A,  they  will  have  something  in  common,  otherwise  they 
could  not  be  thought  together.  The  same  norm  that  defines  A 
will  also  define  7ion-A. 


chapti:h  \' 
The  Natthe  of  Inference 


The  diet ioii.-irifs  have  fouiitl  it  necessary  to  give  a  score  or 
more  of  syuonynis  to  cover  the  many  uses  of  the  word  inference 
by  philosophers  and  laymen.' 

Logicians  have  not  been  so  nnieh  eoneerned  witli  tlie  ambiguity 
in  llie  word,  as  willi  1lie  con! i-adie1  ions  tliat  seem  to  lie  at  tbe 
lieai't  of  tlie  process  of  inference  itself.  Aristotle,  very  early 
in  his  thinking  about  the  fundamental  i)roblems  of  Logic,  dis- 
covered the  paradox  in  all  judgment.  No  term  it  seems,  can 
be  truly  predicated  of  another  tei'm ;  it  can  only  be  predicated 
of  itself.  The  only  true  i)ropositions  are  the  identical  propositions. 
You  can  not  truthfully  afHi'ui  that  '*.l  is  B,"  but  only  that 
"A  is  A."  Tills  dilennna  arises  then,  in  saying  ''A  is  B,"  you 
predicate  what  the  object  A  is  not,  and  you  therefore  speak 
falsely;  but  on  the  other  hand,  if  you  say  "A  is  A,"  you  indeed 
predicate  what  it  is,  but  you  say  nothing  and  the  judgment  is 
idle.  So  thought  vil)rates  betMcen  the  extremes  of  tautology 
and  falsitfj;  apparently  witli  no  jiossibility  of  a  resting  place 
between  the  two. 

Now  while  the  modern  logicians  profess  to  be  seriously  dis- 
1url)ed   l)y  tliis  ancient   dilennna   they   define   infcrotcf  in  ways 


1  Some  of  the  dictioiiarv  syiioiiyiiis  of  inforeiu-o  are:  analysis,  anti- 
cipation, argument,  argumentation,  assay,  assent,  assumption,  eonelusion, 
conjeeture,  conviction,  corollary,  criterion,  decision,  deduction,  demonstra- 
tion, dilemma,  discovery,  elencli,  enthymeme,  examination,  experiment, 
experimentation,  finding,  forecast,  generalization,  guess,  hypothesis,  illa- 
tion, induction,  inquiry,  investigation,  judgment,  lemma,  moral,  persua- 
sion, porism,  ])rediction,  jirevision.  presumjition,  ])rol)ation,  ]>rogno-;tica- 
tion,  proof,  ratiocination,  reasoning,  researidi,  sifting,  surmise,  test, 
theorem,  verdict. 

[81] 


82  FOOTNOTES  TO  FOBMAL  LOGIC 

that  show  they  have  for  the  most  part  ignored  the  paradox. 
The  conclusion  in  any  inference,  mediate  or  immediate,  we  are 
told  in  varying  language  must  be  another,  or  a  new,  or  a  differ- 
ent, or  a  frcsli  proposition.  But  we  find  few  serious  attempts 
to  define  otherness,  newness  or  difference.  Again  we  are  told 
that  inference  is  the  "explication  of  implications,"  or  the 
■ '  passage  from  one  fact  to  another  "  ;  it  must  be  ' '  more  than  vain 
repetition."  Or  it  is  the  "supporting  of  a  judgment  by  its 
reasons,"  the  "discovery  of  necessary  connections,"  "combining 
of  two  premises  so  as  to  cause  a  consequent  conclusion,  or  "draw- 
ing a  conclusion  from  premises. ' '  And  again  none  of  the  essen- 
tial words  are  clearly  defined.  The  writers  often  confess  that 
they  are  employing  the  significant  words  of  their  definition  in 
"new"  ways,  that  the  meanings  that  they  attach  to  them  are  not 
in  conformity  with  ordinary  human  usage.  Hobhouse  suggests 
that  there  is  something  unusual  in  his  use  of  the  word  "new," 
by  continually  writing  it  with  quotations. 

It  will  be  well  to  consider  several  of  the  typical  definitions 
of  inference ;  to  show  how  they  reveal  in  varying  degrees  the 
' '  circle  in  defining. ' '    Adamson  says : 

Inference  is  that  mental  operation  which  j^roceeds  by  combining  two 
premises  so  as  to  cause  a  consequent  conclusion.  Some  suppose  that  we 
may  infer  from  one  premise  by  a  so-called  "immediate  inference."  But 
one  premise  can  only  reproduce  itself  in  another  form,  e.g.,  all  men  are 
some  animals;  therefore  some  animals  are  men.  It  requires  the  combina- 
tion of  at  least  two  premises  to  infer  a  conclusion  different  from  both.- 

Later  we  shall  examine  this  view  that  rejects  the  immediate 
inference.  I  wish  at  this  time  to  point  out  that  the  expression 
"to  cause  a  consequent  conclusion"  is  ambiguous,  redundant, 
and  inclusive.  It  tells  us  only,  at  best,  that  an  inference  is  an 
inference.  And  this  circle  in  defining  lurks  in  all  the  other  defini- 
tions.    According  to  Joseph : 


2  Ency.  Brit.  XVI,  879. 


nil':  NATlllK  OF  ISFERKWE  8:5 

Inference  is  a  process  of  thought  which,  startinj^  with  one  or  more 
ju(]<;enientH,  ends  with  another  judj^ement  made  necessary  by  the  former. 
The  latter,  which  in  relation  to  the  judgement  or  judgements  from  which 
the  process  starts  is  called  conclusion,  which  must  in  comparison  with 
them  be  a  nac  judgement;  to  repeat  in  fresh  words  our  original  statement 
is  not  inference,  any  more  than  translation  is  inference.  For  the  most 
part  a  new  judgement  is  only  got  by  putting  together  two  judgements, 
and,  as  it  were,  extracting  what  they  yield.  But  there  are  a  few  con- 
clusions whioii  we  appear  to  draw,  not  from  any  "putting  together''  of 
two  judgements  but  simply  from  the  relation  to  one  another  V)y  putting 
together  of  the  terms  in  one  judgment.  This  is  called  immediate  infer- 
ence.3 

Welton's  definition  reads:  "Inferenee  oi-  reasoning  is  the 
process  by  which  we  pass  from  affirming  one  or  more  propositions 
to  anotliei-  <h'ff<r<  lit  judgment  wliieh  we  make  as  the  necessary 
I'esult  of  accepting  the  first."  Also,  "Conclusion  states  the  orig- 
inal truth  in  a  new  form. "^  And  again,  "Inference  or  reasoning 
is  the  deriving  of  one  truth  from  another.  By  this  is  meant 
that  tlie  new  judgment  is  accepted  as  true  because,  and  in  so 
far  as,  the  validity  of  the  judgment  from  which  it  is  derived  is 
accepted.'""'  Bosauquet's  much  discussed  definition  is,  ''^Mediate 
judgment  or  inference  is  the  indirect  reference  to  reality  of 
differences  within  a  universal  by  means  of  the  exhibition  of  this 
universal  in  differences  directly  referred  to  reality.""  Miss 
Jones  says.  "One  proposition  is  an  inference  from  another,  or 
others,  when  Ihe  assei-tion  of  tlie  former  is  justipcil  by  the  latter 
and  latter  is,  in  some  respect  different  from  the  former."' 
Windelband  insists  that  ''Inference  is  nothing  else  than  a  way  of 
establishing  judgments,  and  is  indeed  a  judgment  by  means  of 
judgment."'*  This  definition  is  satisfactory  until  we  come  to  see 
that  the  whole  (juestion   at   issue   is  just    the    meaning   of  this 


•'  Introduction  to  Logic  (Oxford,  Clarendon,  1906),  \k  '20;). 

t  Manual  of  Logic  (London,  Clive,  1891),  V,  24. 

■'  Ibid.,  I.  25(5. 

"■•  Logic,  1,  4. 

7  Jones,  E.  E.  C,  Elements  of  Logic  (Edini)urgh.  Claike.  1890).  p.  i:?9. 

■s  Enri/.  Philos.  Sri..  I,  27. 


84  FOOTNOTES  TO  FOBMAL  LOGIC 

process  of  "establishing"  judgments.  Inference  has  very  often 
been  described  as  the  extracting  from  a  proposition  of  its  implied 
meanings,  or  the  explication  of  implications.  But  here  we  have 
again  a  petitio,  for  this  description  presupposes  the  definition  of 
explication  and  implication.  The  symbolic  logicians  have  recogn- 
ized this  inevitable  circle  and  have  for  the  most  part  frankly 
accepted  among  their  indefinable  notions  the  notion  of  impli- 
cation.^ 

One  of  the  commonest  of  all  the  vague  words  which  we  are 
tempted  to  employ  in  the  definition  of  inference  is  the  word 
virtually.  Many  writers  say,  that  if  the  premise  in  an  inference 
only  virtually  contains  the  conclusion,  then,  when  the  conclu- 
sion is  "drawn  from"  or  "extracted  from"  the  premise,  the 
"new"  judgment  at  which  we  arrive  will  be  both  a  different 
way  of  viewing  and  a  different  way  of  expressing  the  same 
truth.  As  a  typical  illustration  of  an  account  of  inference  which 
employs  several  of  these  ambiguous  words  I  cite  the  following 
from  Joseph:  "In  all  inference  there  must  be  some  movement 
of  thought ;  we  nuist  conclude  with  something  not  quite  the  same 
as  what  we  started  with;  though  the  obviousness  of  the  infer- 
ence is  no  ground  for  denying  that  it  is  inference."'"  This 
activity  of  thought  as  it  passes  on  to  a  "fresh"  point  of  view, 
this  step  which  it  takes  as  it  clothes  itself  in  a  "new"  form,  is 
an  inference.  But  such  an  account  I  am  inclined  to  think  does 
not  get  to  the  center  of  the  difficulty.  It  has  solved  the  problem 
by  translating  it  into  a  new  form.  The  vital  question  is,  "What 
is  the  difference  between  a  judgment  that  is  actually  and  one 
that  is  only  virtually  containeel  in  the  premise f  Again  we  may 
ask.  What  have  we  added  to  the  ' '  old ' '  when  we  say  that  thought 
has  been  "active"  in  "stepping"  to  the  new  point  of  view? 


9  e.g.  Russell  says:  "A  definition  of  implication  is  quite  impossible. 
If  p  implies  q,  then  if  p  is  true  q  is  true,  i.e.,  p  's  truth  implies  q  "s  truth ; 
also  if  q  is  false  p  is  false,  i.e.,  g's  falsehood  implies  p's  falsehood.  Thus 
truth  and  falsehood  give  us  merely  new  implications,  not  a  definition  of 
implication."  Principles  of  Mathematics,  p.  14. 

'io  Introduction  to  Logic,  p.  217. 


THE  N ATI- UK  OF  JXFERENCE  85 

When  is  tlic  fliaiif^i'  not  a  step?  It  is  said,  that  llic  obviousnoss 
of  the  step  is  no  ol^jcction  to  callinj^  it  an  inference.  And  again, 
we  liave  on  our  liands  tiic  word  obvious  whieh  is  cpiite  as  vague 
as  virtuaUij,  unr,  old  or  frtsli.  Since  inference  is  not  really  a 
transition  in  time,  it  is  evident  that  a  conclusion  will  not  lose  its 
character  as  inference  as  soon  as  it  becomes  obvious.  Inference 
involves  discovery  but  it  does  not  cease  to  be  inference  when 
(tlie  discovery  having  l)een  made)  thought  vindicates  the  inf<n"- 
ence  by  proof.  As  liosaiKpiet  has  so  well  said.  "Discovery  tvith- 
out  proof  is  conjecture;  an  element  of  proof  is  needed  to  con- 
stitute infei'ence,  and  indeed  to  constitute  discovery.  The  activ- 
ity of  inference  cannot  be  identified  with  the  perception  of 
something  new.  It  is  (piitc  a  noi-mal  oceuri'ciicc  that  the  ele- 
ments which  are  indirectly  referred  to  reality  should  also  be 
directly  referred  to  reality.  "^^ 

Hobhouse  says:  "Any  assertion  is  'new'  (as  eomj)an'd  with 
some  other)  as  long  as  the  two  contents  are  in  any  way  distinct. 
Whatever  the  real  inseparability  of  the  facts,  as  long  as  they  are 
distinct  to  pass  from  the  one  to  the  other  is  to  make  a  new 
assertion."^-  But  it  seems  to  me  that  Hobhouse  has  not  reached 
the  central  issue  either.  To  define  the  "new"  as  that  which  is 
"in  any  way  distinct"  is  hardly  satisfactory.  We  are  at  once 
confronted  with  the  ditficulty  of  showing  how  two  contents  may 
be  regarded  as  distinct  if  they  have,  as  he  declares,  a  real  insepa- 
rability. In  all  his  discussions  of  the  nature  of  thinking,  Hob- 
house has  quite  consistently  maintained  that  it  is  the  primary 
function  of  inference  to  reach  "new"  facts.  But  in  the  last 
aiudysis,  by  "new"  facts  he  means  those  wliicli  have  not  been 
presented  to  the  mind  in  any  previous  sense  perception  or  act 
of  memory.  But  the  past  is  connected  with  the  present  by  a 
continuous  tic;  llicrcfore  predication,  which  always  passes  be- 
yond the  i)rescnt,  can  not  be  ti'uly  novi'l.     Every  theory  of  infer- 


11  Lof/ic,  II,  8. 

12  Hobhouse,  Theory  of  Kttotrlcdgr  (Lomlon,  IMothucn,  1S96),  p.  216. 


86  FOOTNOTES  TO  FOBMAL  LOGIC 

ence  must  finally  go  back  to  the  world-old  Platonic  Doctrine  of 
Kecollection.  Inference  is  the  process  of  discovering  what  we 
already  logically  possess  but  did  not  observe  that  we  possessed 
until  we  psychologically  came  upon  it. 

If  consensus  of  opinion  may  be  taken  as  a  warrant  for  the 
assertion,  the  modern  discussions  as  to  the  nature  of  inference 
have  shown  that  it  must  be  more  than  direct  apprehension,  or 
immediate  experience.  Welton  says,  "Inference  involves  'mental 
process,'  "  and  with  this  others,  for  example  Joseph,  agree. 
They  declare  that  in  all  inference  there  must  be  some  "move- 
ment of  thought. ' '  But  here  again  are  we  not  begging  the  whole 
question?  How  shall  we  decide  when  and  in  what  way  thought 
has  moved?  What  is  to  distinguish  between  a  mental  process 
which  yields  an  inference  and  that  state  of  consciousness  which 
is  not  a  process  and  which  is  therefore  characterized  as  bare 
tautology.  I  confess  that  often  in  these  pages  I  have  myself  had 
to  resort  to  the  expression  "movement  of  thought,"  but  I  have 
tried  to  show  that  these  words  are  meaningless  unless  they 
involve  a  reciprocating  process — forward  and  backward,  analytic 
and  synthetic.  The  paradox  of  inference  does  not  disappear 
when  (as  some  writers  seem  to  think)  we  attach  adjectives  to 
the  terms,  old  and  new,  to  the  inference  and  the  inferend.  We 
are  told  that  the  conclusion  of  an  inference  nu^st  not  be  a  mere 
repetition  of  the  old — that  there  must  be  genuine  novelty.  But 
this  does  not  dissolve  the  paradox.  Any  tautology  is  bare 
tautology  and  any  novelty  is  genuine  novelty. 

The  objection  wliich  INIill  and  after  him,  Adamson  and  others 
have  raised  against  the  immediate  inferences,  namely,  that  there 
is  in  the  conclusion  no  "new"  truth,  will  hold  also  against 
mediate  inferences  and  even  against  induction.  The  attempt  to 
regard  induction  as  different  in  kind  from  deduction  breaks 
down  under  the  weight  of  its  own  inherent  self-contradiction. 
The  logician  who  offers  a  theory  of  induction  that  attempts  the 
self-vindication    of    its    own    processes    has    on    his    hands    this 


Till-:  SATl'IiF.   OF  IXFERENCE  87 

(lilciiiiiia:  citlicf  111'  lai'itly  presupposes  the  universal  li-utlis  and 
liciU'e  Ills  iiielliod  is  not  ttieir  soi<'  soiii'ce,  or.  on  the  othei-  hand, 
they  remain  nnproxed  bceause  his  nictliod  is  confessedly  a  method 
of  probability  only.  The  syllogism,  as  was  pointed  out  hy  its 
earliest  crities,  is  indeed  incompetent  to  supply  its  own  premises. 
P.iit  now.  when  in(hietion  steps  in  to  furnish  deduction  with 
these  univer.sal  truths  for  its  i)remises,  it  is  shackled  by  tlu;  same 
fetters  from  which  it  proposes  to  relieve  deduction.  Induction 
is  itself  a  process  of  reasoning  from  premises,  and  must  obey  the 
fundamental  law  which  ^M)verns  deduction;  the  conclusion  is  ti'ue 
only  if  the  ])i'emises  are  true.  In  a  commendable,  fraternal  spirit, 
induction  would  remove  the  "mote"  from  its  brother's  eye,  dis- 
regarding the  "beam"  in  its  own.  The  synd^olic  logicians  are 
right,  in  my  opinion,  in  theii-  criticism  of  induction.''' 

II 

The  dictionaries,  and  many  of  the  ordinary  textbooks  in 
Logic  have  defined  inference  in  terms  of  judgment  and  judg- 
ment in  terms  of  inference  without  recognizing  or  confessing  the 
"circle."  Many  attempts  have  been  made  by  recent  writers,  to 
establish  either  a  temporal  or  a  logical  i)rioi'ity  in  favor  of  one 
or  the  other.  Such  discussions  have  generally  resulted  in  the 
discovery  that  each  of  these  functions  may  be  taken  either  as 
chronologically  or  logically  prior  to  the  other.  In  attempting 
to  distinguish  between  judgment  and  inference,  we  find  that  the 
ambiguity  between  these  two  words  lias  made  it  possible  for  one 
wi'iter  to  nnd<e  inference  prior  to  judgment  while  anotlier  makes 
judgment  prior  to  inference.     Uotli  judgment  and  inference  as 


13  Cf.  Russell,  Principles  of  Mothcmatics,  p.  11.  "What  is  calleil  induc- 
tion appears  to  me  to  be  either  disguised  deduction  or  a  method  of  mak- 
ing plausible  guesses."  Also  Shearman,  Scope  of  Formal  Logic  (London, 
1911),  p.  xiv.  "In  so  far  as  such  studies  set  forth  methods  of  ]iroof 
the  studies  are  formal  in  cdiaracter,  and  in  so  far  as  they  refer  to  matters 
that  are  proliminarv  to  the  application  of  proof,  thev  are  not  Logic 
at  all." 


88  FOOTNOTES  TO  FOBMAL  LOGIC 

conscious  processes  pass  through  various  stages  of  (lev(^lopni('nt. 
When  we  take  inference  at  its  early,  rudimentary  and  uncon- 
scious beginning,  we  shall  find  it  of  a  lower  order  than  judgment, 
if  at  the  same  time  judgment  is  taken  at  the  highest  stage  of  its 
development.  And  on  the  other  hand  primitive  judgment  is 
needed  as  a  prerequisite  for  overt  inference.  Judgment  is  the 
lower  limit  of  inference  and  inference  is  the  upper  limit  of  judg- 
ment ;  that  is  to  say,  in  judgment  the  given  fact,  the  process  of 
its  justification,  and  the  product  are  merged  into  a  single  state- 
ment. 

Bradley  has  made  the  difference  between  inference  and  judg- 
ment depend  upon  the  directness  or  indirectness  of  the  reference 
of  the  predicate  to  reality.  He  has  defined  judgment  as  the 
direct  reference  of  a  content  to  reality  and  inference  as  the 
indirect  reference  of  a  content  to  reality.  This  is  a  distinction 
that  at  first  sight  seems  very  clear.  But  we  soon  discover  that 
we  have  only  postponed  the  difficulty  and  have  stated  the  orig- 
inal question  in  a  new  form.  When  we  pursue  our  analysis  into 
the  distinction  between  direct  and  indirect  we  seem  soon  to  be 
lost  in  another  maze  of  bewildering  perplexities.  The  essence 
of  Bradley's  doctrine  is  that  whenever,  on  the  strength  of  what 
we  know  about  a  tJiis,  we  make  an  assertion  about  a  ttiat,  we  are 
inferring.  But  as  we  saw  in  a  previous  chapter,  there  is  no 
distinct  and  intelligible  line  of  separation  between  the  tliis  and 
the  tliat.  The  whole  theory  hinges  again  upon  the  distinction 
between  the  explicit  and  implicit  which  is  not  a  distinction  in 
the  form,  but  only  in  the  matter  of  thought.  However,  I  believe 
the  "circle"  is  less  objectionable  in  Bradley's  way  of  distinguish- 
ing between  judgment  and  inference  than  in  any  other. 

Every  judgment  when  called  upon  to  exhibit  its  reasons 
develops  into  an  inference.  This  statement  does  not  refer  to  the 
inductive  process  of  establishing  the  universal  propositions  that 
are  required  for  deduction.  We  have  seen  that  judgment  begins 
its  existence  when  it  is  observed  that  the  predicate  might  have 


TIIK  \.ITl'in<:  OF  ISFEBENCE  89 

been  .soiiicthing  else.  Now  in  on  In-  to  caus('  the  judtriiieiit  to 
become  eonscious  of  its  i-casons  \\c  have  mei-ely  to  hold  in  lliouglit 
a  suggested  coiit  I'adiclory  |)i'c(lica1c  as  a  siibstitut(.'  for  tlie  pi-edi- 
cate  actually  found  in  llic  judgment.  This  ml  mil  predicate,  in 
the  process  of  rejecting  the  p<is.sibl<  predicate,  vindicates  itself 
with  a  brcausr.  Thus  tiie  judgment  "S  is  F"  expands  into  the 
following  ilisjunetive  inference:  ''S  is  either  I'  or  non-I'."  but 
for  such  and  such  I'casons  '*«S'  cannot  be  non-l'."  therefore  **.V  is 
P."  iloreover,  this  fact  that  judgment  vindicates  itself  by 
enlai-ging  into  an  inference  is  another  way  of  stating  the  general 
idealistic  doeti'iiie  that  all  knowledge  is  a  system  of  parts  so  intei'- 
related  that  the  wliolc  ma\'  be  unravelled  fi'oin  \\hate\cr  i)oint 
we  begin. 

As  Hol)house  and  others  have  said,  thei-e  is  no  j)sychologieal 
evidence  that  inference  is  develojH'd  among  the  states  of  con- 
sciousness latei'  than  judgment,  or  that  it  in  any  way  nuikes  use 
of  the  completed  j)rocess  of  a  prior  judgment.  As  soon  as  the 
object  is  presented  to  the  iiiiiid  it  is  stimulate(l  iu)t  only  to  make 
an  aimlysis  of  the  fact  itself  but  also  to  compare  it,  to  notice  its 
position  in  the  system  of  facts,  l^^i-om  simjile  apprehension, 
through  conce{)tion  and  judgment,  to  inference,  the  j)i'Ocess  is 
one  undividml  whole.  IJoth  inference  and  judgment  stai't  with 
something  given.  Each  represents  a  j)articular  way  that  the 
nnnd  has  of  i-eaeting  upon  this  datum.  Judgment  begins  with 
terms  which  it  eitlie]-  aiudyses  or  cond)ines.  The  inference  begins 
with  propositions  which  it  likewise  analyses  oi'  combines.  They 
differ  merely  in  the  chai'acter  of  the  material  upon  which  they 
operate,  and  cousecpu'utly  may  be  said  to  differ  not  at  ail,  or  to 
differ  nuM-ely  in  degree.  In  the  one  case  the  difference  between 
the  datum  and  the  conclusion  is  explicit  and  in  the  other  it  is 
moi'e  or  less  implicit.  Although  they  are  insei)arable  aspects  of 
one  mental  fact,  nevertheless  explicit  judgment  comes  into  con- 
sciousness before  explicit  inference.  Here,  again,  we  imve  an 
illustration    of   that    univei'sal    law    in   the   evolution    of  thought, 


90  FOOTNOTES  TO  FOBMAL  LOGIC 

uamely,  that  we  become  aware  of  the  concrete  result  or  product 
first,  and  the  process  or  law  later. 

A  casual  examination  of  any  instance  of  ''I  think"  reveals 
both  a  forward  and  a  backward  movement  of  thought.  The  one 
movement  is  from  premises  forward  to  conclusion,  the  other  from 
conclusion  back  to  premises  or  "reasons."  In  the  former  case 
we  say  ^'M  is  P  and  S  is  M,  hence,  therefore,  or  consequently  S 
is  P."  This  is  commonly  called  inference.  In  the  other  w-e  say 
''S  is  P"  because,  for  or  since  "M  is  P"  and  ''S  is  M."  This 
is  proof  or  demonstration.  In  discussing  the  nature  of  analysis 
and  synthesis  previously,  I  urged  tlie  importance  of  viewing 
these  tw^o  movements  as  inseparably  correlated  aspects  of  any 
complete  living  thought.  And  again  in  the  matter  of  the  relation 
of  inference  and  proof,  both  are  always  found  together.  There 
is  never  a  forward  movement  of  thought,  that  can  know  itself 
to  be  a  genuine  forward  movement,  if  it  does  not  always  feel 
at  its  center  its  own  latent  backward  movement.  There  is  no 
inference — no  true  discovery — without  proof.  A  discovery  that 
is  bereft  of  this  validating  backward  movement  would  be  pure 
adventure  (if  that  were  possible).  But  now,  analytic  attention 
to  the  thought  process  always  finds  one  of  these  movements  more 
prominent  than  the  otlier.  We  might  employ  the  word  reason 
to  denote  the  combined  forward  and  backward  movement  in  its 
logical  totality.  Then  the  word  inference  might  stand  for  the 
process  of  attaining  a  belief  and  proof  for  the  process  of  sup- 
porting the  belief. 

The  real  problem  at  issue  in  immediate  inference  is  not  the 
determination  of  the  precise  limits  which  any  judgment  places 
upon  the  various  movements  or  aspects  of  its  meaning.  This  is 
transformation  or  what  Bosanquet  has  called  "interpretative 
inference";  it  is  the  determination  of  all  the  w^ays  in  which  the 
predicate  may  be  referred  directly  to  the  subject.  "Substantial 
inference"  we  have  Avhen  we  pass  from  one  content  or  relation 
to  anothei-  indirectlv.     It  is  difficult  to  distinguish  between  a 


THE  N  ATI  HE  OF  I  SI- 1:  niiSCE  91 

direct  and  an  iiidifcct  cci'dTiici-  to  I'cality.  'I'ht-  dill'fiviicc  is 
between  what  wc  set-  and  what  we  (h)  not  sec,  hnt  what  we  nught 
see  from  anotlier  point  of  view.  And  this  is  not  a  distinction 
that  depends  npon  obvionsness  or  iininediacy  in  tlieii-  ordinary 
meaning.  Tnfei-enee  is  a  process  wliieli  clianges  oni-  power  of 
perceiving  the  ohjcet.  DeMorgan  remarks  tliat  "inference  does 
not  give  us  more  than  there  was  there  before,  but  it  may  make 
us  see  more  than  we  saw  before."  The  perfect  mind  makes  no 
distinction  between  direct  and  indirect  reference  to  reality.  It 
is  not  obliged  to  say,  "The  facts  present  are  thus  and  thus, 
therefore  I  should  infer  that  facts  not  present  are  thus  and 
thus.  (Omniscience  does  not  have  to  compare  facts  in  order  to 
know  them.)  It  has  what  might  be  called  a  unito-multiple  point 
of  view,  from  which  the  difference  between  the  direct  and  the 
indirect  insight  disappears.  It  does  not  have  to  run  around  an 
object  to  see  how  it  looks  on  the  other  side ;  it  sees  both  sides  at 
once. 

Ill 

The  attacks  on  Formal  Logic  invarial)ly  proceed  ui)on  a  mis- 
taken understanding  of  the  manner  in  which  the  idealist  thinks 
of  the  relation  between  form  and  matter.  Since  Hegel,  many 
logicians  have  reaffirmed  his  doctrine  of  the  essential  correlativ- 
ity  of  these  two  aspects  of  reality.  We  have  come  to  see  that 
form  and  uuitter  do  not  exist  separately,  nor  can  they  even  be 
considered  entirely  apart  from  each  other.  We  should  not  think 
of  them  as  we  think  of  the  seal  and  the  Avax  in  the  classic  illus- 
tration of  form  and  matter.  And  yet  we  may  speak  of  the  form 
of  reasoning  as  being  different  from  its  matter,  without  con- 
tradiction. In  truth,  while  there  is  no  linal  and  completi'  sepa- 
ration of  matter  from  form,  there  is  yet  a  dift'erence  amounting 
to  a  relative  distinction.  Although  the  two  are  not  a  separated 
twain,  tliey  are  nevertheless  separable.  They  are,  in  fact,  inde- 
pendent varial)lt's  within  tlieir  correlation.     The  mathematician 


92  FOOTNOTED  TO  FOBMAL  LOGIC 

has  to  deal  often  with  such  binary  systems  of  independent 
variables.  In  the  world  of  sensory  facts,  too,  we  frequently  find 
one  and  the  same  form  encompassing  a  variety  of  contents  at 
different  times  and  places,  and  on  the  otlier  hand,  the  same  con- 
tent manifests  itself  in  a  variety  of  forms,  iloreover  the  inde- 
pendent variability  goes  so  far,  paradoxical  as  it  may  seem,  as  to 
permit  the  one  to  pass  into  the  other.  What  is  form  in  one  rela- 
tion becomes  matter  in  another  relation.  This  latter  truth  is 
of  the  greatest  importance  for  the  right  understanding  of  the 
theory  of  thought  that  in  current  discussion  calls  itself  dynamic 
idealism. 

The  serious  question  for  Formal  Logic  is  whether,  in  this 
correlation,  we  can  ever  escape  the  necessity  of  defining  each  by 
the  other.  There  are  many  such  circular  definitions;  for 
example,  form  is  that  which  remains  permanent  when  the  matter 
changes  and  matter  is  that  which  remains  permanent  when  form 
changes.  It  has  often  been  remarked  that  all  reasoning  is  in  the 
last  analysis  circular,  that  no  definition  can  escape  the  indict- 
ment of  begging  the  question.  But  whatever  position  one  may 
take  on  the  vexed  question  as  to  the  possibility  of  transcending 
reciprocal  relations  in  definition  and  description,  we  may  yet 
maintain  that  ih ought  itself  does  pass  from  thesis  to  antithesis 
and  thence  to  synthesis,  although  language  may  lag  behind.  The 
third  stage  of  genuine  synthesis,  that  is,  the  synthesis  that  does 
not  itself  in  turn  require  an  antithesis,  must  elude  logical  defini- 
tion. Here  it  may  be  said  is  an  instance  of  a  judgment  tjiat  has 
no  exact  counterpart  in  the  realm  of  propositions;  vocabulary 
has  not  followed  thought.  Now  the  thought  which  reconciles 
the  contrasting  correlation  of  form  and  matter  can  only  be 
described  by  again  employing  the  word,  form.  The  Real  Logic — 
the  contemned  Logic  ilherhaupt — would  be  concerned  with  this 
form.  This  is  what  idealism  has  always  meant  by  the  synthesis 
of  opposites  in  higher  unities.  It  has  not  meant,  for  example, 
that  good  is  bad,  or  that  past  is  present,  etc.,  but  that  these 


////•;  S ATI' HE  OF  IXFKBENCE  93 

coiTclativi's  liavr  soiuctliiii^  in  coiiiiiioii.  In  liki-  manner  there 
must  he  somd  liin<^  in  common  l)('1\\iiii  ilir  t'onu  ami  matter  of 
thouglit.''  l>ut  it  must  not  he  sii|)])()sr(l  t  hat  we  arc  Ih-i-c  i-cat'fir-m- 
ing  the  very  old  view  that  the  form  is  always  tlie  constant  and 
the  inattei"  the  changing  characteristic.  As  I  have  just  said  the 
form  may  change  and  the  matter  remain  fixed,  or  the  matter  may 
change  and  the  foim  iriiiaiii  tixed,  oi-  finally  both  foi'iii  and  mat- 
ter' may  vary.  A  wave,  for  instance,  at  no  two  moments  of  its 
life  history  has  either  the  same  form  or  the  same  content.  Yet 
the  wave  unquestionably  has  an  identity  that  persists  amidst  its 
changing  form  and  matter.  It  is  an  individual  Ix-causc  it  is  the 
object  of  a  will-attitude. 

Since  the  time  of  the  givat  Stagirite,  logic  has  been  looked  at 
under  two  aspects:  (1)  real  logic,  (2)  formal  logic.  Both  of 
these  expressions  are  full  of  ambiguities — ambiguities  tiiat  are, 
however,  hardly  avoidable.  Real  Logic  deals  with  the  problem 
of  corrcspondcncf,  Foi'mal  Logic  with  the  problem  of  consistency. 
The  truth  of  correspondence  joined  with  tin-  truth  of  consistency 
constitute  total  reasonableness.  The  question  at  issue  is  whether 
these  two  aspects  enter  into  total  reasonableness  in  different 
degrees  of  importance.  Can  the  question  of  coherence  be 
divorced  fi'om  the  question  of  correspondence?  Is  correspond- 
ence, at  last,  a  kind  of  coherence  ?  These  two  main  senses  in 
which  we  may  speak  of  the  validity  of  thought,  have  been  the 
j)ivotal  i)oints  around  which  the  recent  discussions  regarding  the 
nature  of  infei'cnee  have  revolved.  The  Instrumental  Logic  of 
today  denies  that  there  are  these  two  aspects;  it  dispenses  entii'ely 
with  the  ontological  i)i'ol)lem.     Idealism  has  always  insisted  on 


!■*  Winflell)anil  has  cloarly  recognized  the  necessity  of  distinguishing 
between  tliese  two  points  of  view.  "The  two  kinds  of  categories  may  be 
distinguislied  as  transcendent  and  immanent  in  their  relation  to  truth;  so 
that  I  would  say  that  the  constitutive  categories  are  existential  and  the 
reflective  are  valiil.  It  is  tlie  final  task  of  the  system  of  categories  to 
reunite  the  two  divided  series  and  to  discover  the  forms  of  thought  in  which 
the  two  fundamental  categories,  the  valid  and  the  existential,  are  condiined 
into  a  unitv. "     Enri/.  Fliilos.  Sci.,  I,  35. 


9i  FOOTNOTES  TO  FORMAL  LOGIC 

the  distinction  between  the  ontologieal  and  the  episteniological 
problem,  even  when  (as  in  the  case  of  Hegel)  it  asserts  that 
Dcnkenlekrc  isf  audi  Seinlehre.  It  declares  that  the  relation  of 
thought  to  reality  is  a  real  problem,  and  that  the  recent  attempts 
to  solve  it  by  saying  that  there  is  no  such  problem  or  by  asserting 
that  it  is  of  no  consequence,  is  a  profound  error 

The  question,  "Is  this  particular  instance  of  reasoning 
accurate  ? "  is  at  heart,  always  a  duplex  question.  Although  for 
practical  purposes  we  may  ignore  one  or  the  other  of  these  two 
aspects,  rigorous  thought  demands  that  we  make  the  distinction. 
We  may  have  had  in  mind  to  ask  whether  the  inference  is  itself 
a  manner  of  Being — whether  we  have  laid  hold  of  the  real  nature 
of  things  through  this  mental  operation.  In  the  second  aspect 
of  the  duplex  question,  we  disregard  coincidence  with  reality 
entirely ;  we  wish  merely  to  know  if  our  conclusion  does  follow 
from  the  premises  in  accordance  with  non-contradictory  princi- 
ples. In  the  face  of  all  these  recent  indictments  we  still  declare 
that  Formal  Logic  is  the  science  of  that  part  of  reason  which 
is  concerned  not  with  total  reality  and  complete  reasonableness 
but  with  the  trutli  which  is  contained  in  consistency.  Consist- 
ency is  a  part  of  truth,  necessarily,  but  it  is  only  a  minor  part. 

The  form  of  thought  is  unanalyzable  and  indefinable.  The 
best  we  can  say  of  it  is  that  it  is  the  mode  or  manner  in  which 
thought  is.  It  is  not  an  external  matrix,  independent  of  thought, 
but  is  natural  to  thought.  It  is  intrinsic  in  the  nature  of  thought 
itself,  and  in  so  far  it  is  an  expression  of  that  nature.  But  it  is 
not  a  complete  expression,  any  more  than  the  form  of  a  statue 
is  a  complete  expression  of  the  statue.  It  is.  however,  a  genuine 
expression  of  the  inner  life  of  thought;  an  expression  that  is 
spontaneously  taken  by  thought.  To  say  that  thought  is  deter- 
mined by  this  form  is  inaccurate  and  insufficient.  "What  we 
mean  to  say  is  that  thought  is  self -determining  in  its  form.  The 
form  of  thought  is  essential  to  thought,  though  not  equivalent  to 
the  fulness  of  thought :  thought  does  not  subsist  without  thought- 


THE  NATfli'l-:  or  ISFEBENCE  95 

form.  Thought,  as  thouglit,  has  tliis  form,  and  without  it  tliought 
in  so  far  is  non-existent.  The  form  of  tlionght  is  peculiar  and 
untranshitahle.  Serious  iiiisuiidcisl;iiidin<r  has  arisen  from  the 
"wax  and  seal"  illustration  of  matter  and  form  of  thought.  It 
would  be  well  if  this  and  all  other  similar  figures  of  speech 
could  be  expunged  from  logical  discussions.  These  similes  are 
largely  responsible  for  confusion  of  hujical  form  with  temporal 
sequence  or  spatial  arrangement. 

Furthermore,  logical  form  is  not  the  same  as  that  sometliing 
ill  objects  that  we  call  the  heautiful  nor  is  it  that  other  some- 
thing in  objects  that  we  call  the  good.  We  cannot  escape  the 
conclusion  that  there  exist  in  consciousness  more  than  one  prin- 
ciple of  arrangement.  But  this  admission  nnist  not  be  regarded 
an  abaiKlouiiient  of  our  defense  of  Formal  Logic.  The  elements 
in  a  certain  sort  of  consciousness  are  arranged  in  a  particular 
way,  while  the  elements  in  another  sort  of  consciousness  are 
arranged  in  another  way.  We  have  the  time-principle,  and  the 
space-principle,  both  existing  and  acting  together  in  conscious- 
ness. Also  we  have  the  esthetic  and  i\\e. moral  principle.  Things 
may  be  satisfactorily  arranged  in  regard  to  time  and  space,  but 
yet  not  be  beautiful ;  or  they  be  harmonious  as  regards  the 
esthetic  principle,  and  still  be  lacking  in  goodness. 

But  there  is  yet  another  princii)le  that  we  must  add  to  the 
foregoing  list.  Betw^een  the  time  and  the  space  principle  on  the 
one  hand,  and  the  esthetic  and  the  moral  principle  on  the  other, 
comes  the  truth  principle,  and  it  this  principle  with  which 
Formal  Logic  is  concerned.  Thus  we  get  the  whole  series  of  the 
iiv(  principles  of  estimah  .  in  whicli  series  the  logic-principle  is 
tile  tliird.  There  are  two  aspects  to  this  third  prineijile:  in  its 
highest  aspect,  the  logical  principle  is  that  of  truth  absolute  and 
entire;  in  its  other  aspect  it  is  susceptible  of  degree.  It  is  not 
in  contradiction  to  what  I  have  asserted  elsewhere  to  say  that 
the  principle  of  reality  or  truth  has  degree:  tliat  a  state  of  judg- 
ment may  lie  on  tlie  wa\'  to  tlie  goal  of  complete  truth  and  jier- 


96  FOOTNOTES  TO  FOBMAL  LOGIC 

feet  reality,  just  as  a  thing  may  be  on  the  way  to  the  goal  of 
beauty  or  of  goodness. 

The  new  positivism  which  postulates  a  world  of  independent 
objects — brute  facts — rests  back  upon  an  unwarranted  abstrac- 
tion. It  has  taken  this  fundamental  relation  between  form  and 
matter  and  pressed  the  correlation  to  the  point  of  breaking. 
The  matter  of  thought  is  something  that  is  finally  foreign  or 
indifferent  to  its  form.  This  indifference  constitutes  its  inde- 
pendence, since  that  aspect  of  thought  which  is  indifferent  to  a 
changing  aspect,  it  would  appear,  cannot  be  otherwise  than  inde- 
pendent. The  fallacy  in  this  reasoning,  is  due  to  a  false  analogy. 
In  the  physical  world,  matter  does  lie  in  the  form,  like  the 
pudding  in  the  mould.  But  the  form  of  thought  is  not  something 
that  is  laid  over  the  matter  nor  is  the  matter  anything  injected 
into  the  form.  The  form  is  only  the  class  of  relations  in  which 
the  essential  na,twre  of  matter  may  stand.  The  systematic  view 
of  the  ways  in  which  its  inner  relations  may  express  themselves  is 
thought's  form. 

It  is  unfair  to  the  Traditional  Logic  to  say  that  it  has  divorced 
form  from  matter,  that  it  has  not  held  form  in  abeyance  and 
obliged  it  to  wait  upon  matter.  No  one  has  been  more  explicit 
on  this  point  than  Bosanquet  who  says,  "We  cannot  and  must 
not  exclude  from  the  form  of  knowledge  its  modifications  accord- 
ing to  'matter'  and  its  nature  as  existing  only  in  'matter.'  "^'^ 
Again  Joseph  has  said :  ' '  The  form"  and  content  of  thought  are 
not  capable  of  separate  consideration,  like  the  mould  and  the 
pudding;  what  from  one  point  of  view  is  form  is  from  another 
matter,  and  the  same  form  in  different  kinds  of  content  is  not 
altogether  the  same,  any  more  than  is  the  same  genus  in  different 
species."^" 

It  is  often  believed  that  any  successful  indictment  of  the 
syllogism  will  carry  with  it  the  condemnation  of  Formal  Logic, 


15  Essentials  of  Lofjic,  p.  50. 
'^C'  Ititroduclioii  to  Logic,  p.  214. 


THE  SATl'UE  OF  INFERENCE  97 

as  a  whole.  But  this  docs  not  folhnv.  The  two  docti-iiics  are  not 
so  intcidcpendent  thai  they  must  stand  oi-  fall  together.  We 
may,  with  Bradkn',  ch-ny  the  iiniverality  of  the  syHogism,  and 
still  hold  that  "all  reasoning  is  formal  and  is  valid  solely  by 
virtue  of  its  form."  Every  inference  belongs  to  a  class.  It 
has  its  own  type,  and  it  moves  in  accordance  with  a  pi'inciple  that 
governs  not  oidy  it,  but  all  other  members  of  its  class.  Bradley 
is-(iuite  sure,  liowevei",  tliat  we  can  never  determine  the  class  of 
all  such  classes.''  Jjut  this  denial  that  there  is  a  universal  form 
of  thought  is  itself  just  the  final  type  for  which  we  are  looking. 
1  confess  that  1  see  no  otiiei"  than  the  familiar  traditional  answer 
to  this  difficulty.  The  agnostic  who  says  there  are  no  final  formal 
princijiles  is  asserting  that  there  is  at  least  one  such  pi-inciple, 
namely,  the  principle  that  declares  that  there  are  no  principles. 
It  is  alleged  that  we  cannot  understand  fully  the  es.sential 
nature  of  the  thinking  process  if  we  operate  merely  with  symbols. 
The  foiiii  of  thought  is  vitally  affected  by  that  which  is  thought 
about.  But  the  opponents  of  Formal  Logic  ignore  a  distinction 
that  is  of  very  ancient  origin,  namely,  the  distinction  between  the 
two  kinds  of  assertion  that  we  may  make.  We  either  assert  a 
relation  between  things  (or  the  attributes  or  condition  of  things), 
or  else  we  assert  a  relation  between  assertions.  This  distinction 
between  material  implication  and  formal  implication  furnishes 
tlie  incontestable  basis  for  Symholic  Logic.  The  calculus  of 
propositions — formal  implication — is  a  study  tliat  nuiy  be  pur- 
sued inde]iendeutly  of  any  other  implication. 


IV 

Many  of  the  attempts  that  have  been  nuide  to  reconcile  the 
empirical  and  the  idealistic  theories  of  the  relation  between  the 


'^'^  Principles  of  Logic,  p.  471.  "No  possible  logic  can  supply  us  with 
schemes  of  inference.  You  may  have  classes  and  kinds  and  examples  of 
reasoning,  hut  you  can  not  have  a  set  of  exhaustive  types.  The  conclusion 
refuses  siiuiily  to  fill  up  the  blanks  you  haxc  supplied." 


98  FOOTNOTES  TO  FOBMAL  LOGIC 

universal  and  the  i)articulai'  in  thought  have  been  reconciliations 
in  name  only.  They  have  generally  allowed  the  opposing  theories 
to  make  assertions  that  are  logically  contradictory.  And  when 
the  pacifier  happens  to  be  one  of  the  contesting  parties,  the  recon- 
ciliation that  is  effected  involves  the  annihilation  of  his  opponent. 
But  also,  equally  unsatisfactory  has  been  the  reconciliation  when 
the  third,  or  benevolent  neutral  party,  has  stepped  in.  He  has 
generally  cancelled  all  the  outstanding  differences  between  them, 
and  left  the  two  theories  standing  "harmoniously"  side  by  side 
in  the  night  of  thought  in  which  all  cows  are  gray.  Obviously  the 
idealist  may  accept  no  terms  of  peace  which  would  deprive  reason- 
ing of  its  universal  character.  Nor  may  the  empiricist  abandon 
his  own  central  contention  that  all  reasoning  is  from  particular 
to  particular.  The  empiricist  begins  with  the  sense-presented 
particular,  and  proceeds  thence  in  quest  of  the  universal.  Failing, 
however,  to  reach  this  goal  by  the  way  of  the  accunuilation  of 
particulars — the  only  pathway  he  recognizes — he  boldly  declares 
that  the  universal  (even  if  it  could  be  reached)  would  not  be 
needed.  All  reasoning  is  from  particular  to  particular,  the 
universal  is  a  convenience  not  a  necessity. 

The  relation  between  the  particulars  and  the  universal  may 
be  read  off  in  three  ways.  We  may  read  it  (1)  from  particular 
to  universal,  (2)  from  universal  to  particular,  or  (3)  from  par- 
ticular to  particular.  It  would  seem  therefore  that  there  must 
be  as  many  different  kinds  of  thinking  as  there  are  possible 
relations  here.  Now  Aristotle  did  clearly  recognize  this  three- 
fold relationship  and  on  the  basis  of  these  distinctions  declare 
that  there  were  three  kinds  of  thinking.  Reasoning  from  par- 
ticular to  particular  he  called  7rapd8€t^/u.a,  reasoning  from  par- 
ticular to  universal  eTrajcovr],  and  finally  reasoning  from 
universal  to  particular,  avWo'yta/jio'i.  But  Aristotle  was  not  will- 
ing to  give  to  each  of  these  types  an  independent  or  coordinate 
function  in  knowledge.  Although  he  recognized  the  importance 
of  analogy  and  induction,  he  was  firmly  convinced  that  these 


rilF.   SATrilE  OF  IXFKUKM  F.  99 

wci'c  merely  opei-alioiis  subsidiary  to  real  tiiinkiug  wiiieii  in  the 
last  analysis  was  always  syllogistic.  Professor  Adamson  and 
others  have  accepted  Aristotle's  threefold  relatioiislii]*  hiil  have 
set  up  thi-eo  independent  tyjx'S  of  inference:  namely,  (Ij  from 
particular  to  partieulai-,  analogical  infei'ence;  (2)  from  par- 
tieiilai-  to  iiiii\crsal,  imluctive  inference;  (3)  from  universal  to 
particular,  tleductive  or  syllogistic  inference.  But  I  shall  insist 
that  each  of  these  types  of  i-easoning  expresses  only  in  a  partial 
and  one-directional  \\a.\  the  reciprocating  thought  process  that  is 
at  the  basis  of  all  llii'ee. 

Adamson'^  has  maintained  that  all  inference  is  mediate.  But 
in  setting  up  these  three  types  of  reasoning  he  has  apparently 
denied  the  necessity  of  mediation.  In  his  account,  each  form 
of  thinking  deals  with  two  tei-ms  oidy.  iJut  on  closer  examina- 
tion We  find  thai  <'acli  of  these  binary  i-elations.  fi'om  pai'ticular 
to  uuivei-sal,  from  universal  to  i)articular,  from  ])articulai'  to 
pai'ticular,  has  in  I'eality  a  suppressed  third  term.  When  this 
third  term  is  properly  supplied  in  each  instance  we  discover  that 
the  three  forms  of  I'casoning  are  really  at  bottom  the  same.  No 
reasoning  is  merely  from  particular  to  universal,  nor  from 
universal  to  partieulai',  noi-  fi-om  jjartieular  to  ])articular.  l)Ut 
in  any  complete  act  of  reasoning  we  are  always  passing  from 
particular  to  particular  via  the  universal.^"  This  pervading 
identity  is  to  be  sure  not  always  nor  often  overtly  operative; 
therefore  by  the  popular  mind  and  in  some  systems  of  jjhilosophy 
it  is  declared  to  be  totally  absent.  Wherevei"  thei-e  ap])ears  to 
be  inference  from  particular  to  particular  it  is  because  we  do  not 
take  the  trouble  to  state  the  ground,  either  because,  on  the  one 


18  "We  may  proceed  either  directly  from  particular  to  particular  l>y 
analogical  inference,  or  indirectly  from  particular  through  universal  to 
particular  by  an  inductive-deductive  infoienco  which  might  be  called 
'perduction. '  On  the  whole,  then,  analogical,  inductive  and  deductive 
inferences  are  not  the  same  but  three  similar  and  closely  connected 
processes."  Ency.  Brit.,  XVT,  8S0. 

10  Cf.  Bosanquet,  Logic,  TI,  30.  "The  conception  of  inference  from 
particulars  to  particulars  is  thus  an  illusion  arising  from  the  activity  in 
inference  of  presupposed,   superficial,  or   uiianalysed   universals." 


100  FOOTNOTES  TO  FOIiMAL  LOGIC 

hand,  it  is  so  manifest  or  for  the  opposite  reason,  because  it  is 
not  immediately  in  view. 

Consciousness  is  at  first  neither  of  a  particular  seen  as  a  par- 
ticular, nor  of  a  universal  seen  as  a  universal.  It  is  rather  an 
indistinct  blending  of  the  two.  Succeeding  pulsations  of  con- 
sciousness are  required  to  differentiate  this  confused  i^rimitive 
perception  into  one  or  the  other.  Our  earliest  sense  experiences 
are  definitely  situated  in  space  and  in  time.  Every  perception 
is  present  here  and  now,  and  furthermore  has  its  causal  explana- 
tion. This  would  seem  to  bestow  on  it  individuality,  but  neither 
space  nor  time  are  real  principles  of  individualism.  If  spatial 
and  temporal  relations  were  the  only  distinguishing  character- 
istics, we  should  never  be  able  to  declare  that  the  object  of  a 
present  perception  had  not  been  seen  elsewhere  or  at  another 
time.  The  perception  of  the  individual  or  the  universal  as  such 
is  impossible.  They  are  differentiated  aspects  of  a  dual  act  of 
consciousness.  This  two-edged  act  of  consciousness  is  on  one 
side  the  discovery  of  certain  attributes  as  uniquely  characteristic 
of  one  object  and  other  attributes  as  common  to  many  objects. 
The  x)articulars  with  which  the  empiricist  deals  are  not  really 
particulars,  they  are  the  differences  in  which  the  universal  has 
exhibited  itself. 

Thought,  then,  always  operates  by  means  of  a  universal. 
Furthermore,  we  do  not  tlinl-  unless  in  knowing  the  part  we  do 
also  in  a  sense  know  the  whole.  All  of  our  previous  and  sub- 
sequent discussion  turns  upon  this  principle.  Reasoning  is  never 
from  particular  to  particular.  There  is  no  thoroughfare  from 
one  fact  to  another  fact,  except  by  the  way  of  the  universal.  It 
is  true  that  in  the  psychological  analysis  of  the  process  we  cannot 
discern  the  ascent  to  the  universal  nor  the  descent  from  the  uni- 
versal. We  see  only  an  apparent  transition  directly  from  par- 
ticular to  particular.  But  the  logical  analysis  always  discovers 
the  necessity  of  the  universal.  Reasoning  can  not  possibly  take 
place  unless  there  is  a  universal  within  which  the  particulars, 


77/ A   \.iTli:h  OF  ISI'KHESCE  101 

hetwrni  which  thoiiglit  takes  place,  arc  embraced.  If  each 
so-called  i)articular  wei-e  lo(;ked  up  within  tlie  narrow  limits  of 
its  own  specific  constitution,  it  would  lie  idle  to  talk  ahout  j)ass- 
ing  from  one  such  particidar  to  another.  Yet  this  is  the  assump- 
tion from  which  every  form  of  associational  theory  of  thought 
sets  out.  Each  idea  reproduces  in  the  content  of  another  idea, 
not  oidy  itself,  hut  in  some  mysterious  way  i)roduces  also  the 
connecting  link  between  itself  and  that  other  idea. 

Furthermore,  it  can  be  shown  that  the  empiricist  is  deluded 
in  his  belief  that  he  can  make  an  assertion  that  is  absolutely 
particular.  No  judgment  has  ever  for  its  subject-matter  just 
bare  concrete  fact.  A  particular  judgment  would  be  no  judg- 
ment, because  as  Bradley  has  said,  the  sul)ject  woidd  be  "com- 
pletely shut  up  and  confined  in  the  predicate."  Sucli  a  judg- 
ment might  almost  be  said  to  be  a  stage  prior  to  bare  tautology, 
it  would  tell  us  nothing  else  about  tlio  subject  or  predicate  than 
that  each  is  just  what  it  is. 

We  may,  therefore,  deny  Mill's  contention  that  "the  child 
who  having  burnt  his  fingei's,  avoids  thi'usting  them  again  into 
the  fire,  has  reasoned  or  inferred,  though  he  never  thought  of  the 
general  maxim,  fire  burns."  When  the  child  avoids  thrusting 
his  fingers  into  the  second  fire,  what  wai'us  it  away  is  not  the 
sight  of  the  second  fire,  as  a  bare  isolatt'd  particular.  If  there 
were  no  more  to  this  second  fire  than  just  its  bare  identical  self, 
the  child  would,  of  course,  put  its  fingers  into  the  flame  and  be 
burned  again.  But  the  second  fire  is  something  more  than  just 
a  particular,  it  has  something  over  and  above  its  thisncss.  That 
from  which  the  child  withdraws  its  fingers  is  in  reality  the  first 
fire,  wliicli  it  sees,  by  memory,  in  the  second  fire.  If  it  shoidd 
put  its  finger  into  the  second  fire  and  be  burned,  we  should  chide 
it  with  "You  didn't  think,"  which  for  the  purpose  of  the  defense 
of  the  universal,  I  concede  is  equivalent  to  "You  didn't  remem- 
ber." We  avoid  tlie  issue  wlu'U  we  describe  reasoning  as  a 
passage  from  particular  to  particular,  and  liliidc  at  the  universal 


102  FOOTNOTES  TO  FOBMAL  LOGIC 

Avhich  stares  at  us  from  behind  the  wouhl-be  particular.  The 
object  of  knowledge  is  never  a  pure  this,  it  always  has  a  fringe 
of  thatness. 

]\Iill  and  the  later-day  associationists  have  said  that  "what 
justifies  the  transition  from  one  particular  to  another  is  the 
resemblance  between  the  two  particulars. ' '  We  reason  by  means 
of  the  qualities  which  the  two  have  in  common.  But  this  recogni- 
tion, in  the  second  particular,  of  the  attributes  which  had  pre- 
viously been  found  in  the  first,  is  the  tacit  admission  of  the 
universal  for  which  we  are  contending.  In  the  actual  thought  of 
the  moment  we  may  not  consciously  distinguish  the  universal 
from  the  concrete  instance  in  which  it  is  manifested.  Never- 
theless, subsequent  reflection  discovers  that  the  general  idea  is 
always  there  and  constitutes  the  only  bridge  by  means  of  which 
we  can  reason  from  particular  to  i^articular.-'^ 


20  Cf.  Bradley,  PrincipJes  of  Logic,  p.  36.  "It  is  not  true  that  par- 
ticular images  are  ever  associated.  It  is  not  true  that  among  lower 
animals  universal  ideas  are  never  used.  What  is  never  used  is  a  par- 
ticular idea,  and,  as  for  association,  nothing  ever  is  associated  without 
in  the  process  being  shorn  of  particularity." 


CHAPTER  VI 
IMMEDIATE  INFERENCE 

I 

Before  eonsidci-ing  tlie  ((uestiou  of  the  validity  of  immediate 
inference,  I  wisli  to  otter  a  revision  of  the  names  for  the  entire 
system  of  tlic  so-called  immediate  inferences.  Assuming  that 
objects  corresponding,  to  N  and  P  do  t^xist,  and  furthei-more  that 
these  classes  do  not  exliausl  the  ciilire  universe,  then  tlie  various 
relations  in  tlic  iiiiivci'sal  at'linnative  proposition  ""All  N  is  /'." 
may  be  illustrated  by  the  following  diagram.  Tlie  ol)jeetions  to 
"Euler's  circles"  have  now  been  pi-esented  over-many  times. 
No  one  who  has  ever  taught  elementary  logic  is  unmindful  that 
the  circle  notation  is  incompetent  to  expres;^  i)roperly  the  rela- 
tion between  species  and  genus.  The  genus  is  not  a  class  that  is 
divided  up  into  sections  called  species.  Euler's  diagrams  we 
all  know  apply  oidy  to  the  static  relations  of  inclusion  and  exclu- 
sion. They  are  of  service  only  in  the  calculus  of  classes  and  their 
utility  is  entirely  illustrative.  They  give  no  truths  which  could 
not  have  been  secured  without  their  assistance.  But  they  are. of 
the  highest  service  to  students  in  elementary  logic  for  the  i)roper 
understanding  of  the  i-elations  within  llie  sphere  where  iliey  are 
applicable. 

These  relations  between  two  classes  and  their  negatives  have 
long  been  recognized  and  several  different  ways  of  nanung  them 
have  been  suggested.  In  pi-esenting  this  subject  to  elementary 
students  it  is  certainly  conducive  to  clarity  to  have  one  name 
stand  for  one  only  of  these  relations,  and  to  have  each  of  the 
relations  designated  by  a  single  term.  In  tlie  majority  of  the 
systems  of  the   names  so  far  offered,  this  has   not   always  been 


104 


FOOTNOTES  TO  FOBMAL  LOGIC 


observed.  The  most  of  the  names  which  I  liave  pi"0i)0sed  have 
already  been  employed  by  different  writers,  but  I  am  not  aware 
that  any  one  has  offered  just  this  arrangement.  If  all  of  these 
relations  had  now  for  the  first  time  been  discovered  simultane- 
ously, and  a  committee  of  philologists  and  logicians  were  set  the 


OppositivG    s 


task  of  naming  them,  doubtless  words  derived  from  verfo  Avould 
be  used  throughout,  and  probably  some  attempt  would  be  made 
to  employ  in  each  instance  a  word  more  or  less  suggestive  of  the 
relations  involved.  I  know  of  only  one  attempt  to  construct  such 
a  simple  and  uniform  terminology — that  of  ]\Iiss  Jones.^ 

A  most  radical  departure  was  proposed  by  Miss  Jones,  in 
substituting  reverse  for  eonverse.     If  as  I  have  said,  these  rela- 


1  EJcmoits  of  Logic,  p.  l-io. 


/.)/ .1/ i:i)l.l  TK  IXFEEENCE  10;j 

lions  Were  named  d(  novu,  \n-o\yd\Ay  Miss  Jones'  suggestions 
would  bo  adopted.  Reverse  does  suggest  better  than  converse 
llie  proeess  of  reading'  a  pidposition  ofT"  fi'oiii  its  predicate  end. 
But  tiie  two  names  ronci  rsc  and  contraijositivc  iiave  been  sanc- 
tioned now  by  so  many  generations  of  usage  that  it  would  be 
well-nigh  impossible  to  make  such  a  change.  No  one,  so  far  as 
I  am  aware,  has  adopted  Miss  Jones'  suggestion.  For  tiiese  two 
fundamental  relations  I  have  therefore  accepted  the  names  of 
establislied  usage.  Each  of  the  other  names  which  I  have  assigned 
to  the  various  relations  I  have  found  emi)loyed  by  some  writer, 
with  the  excej)tion  of  oppositive.  In  Keynes-  admirable  elassi- 
Hcation  and  naming  of  the  immediate  inferences,  which  has 
been  followed  by  Creighton  and  others,  some  of  the  relations  have 
compound  designations,  as  ohvcrtcd  converse,  partial  contraposi- 
tive,  etc.  Other  writers  have  employed  long  and  awkward  expres- 
sions for  some  of  the  relations,  for  example,  ''iunnediate  infer- 
ence by  privative  conception" — the  name  given  to  the  ol)verse 
by  Jevons. 

It  would  be  interesting  to  ask  which  of  these  immediate  infer- 
ences the  mind  passes  to  first.  Tiie  ordinary  view  is  that,  from 
the  original  we  step  first  either  to  the  converse  or  the  obverse  and 
proceed  thence  by  successive  obversions  and  conversions  to  the 
others.  But  if  these  other  relations  are  all  immediate  inferences 
we  should  be  able  to  ])ass  directly  to  them  from  the  original.  If, 
however,  there  are  two  or  more  pulsations  of  thought  in  passing 
out  to  the  more  remote  inferences  they  ought  not  to  be  called 
immediate.  In  discussing  the  nature  of  judgment  I  have  already 
contended  that  all  thought  is  in  a  sense  mediate,  that  every  judg- 
ment is  in  tile  end  an  euthymeme.  If  the  original  proposition  is 
an  abbreviated  syllogism,  and  if  each  of  the  inferences  is  like- 
wise an  enthymeme,  then  the  true  explanation  of  the  entire  sys- 
tem of  immediate  inferences  will  be  found  in  the  fundamental 
conception  of  the  syllogism  wliieli  1  sliall  propose  later,  namely. 


2  Formal  Logic,  p.  140. 


106  FOOTNOTES  TO  FOBMAL  LOGIC 

thought  manifesting  itself  through  the  threefold  relation  of 
genus,  species,  and  particular.  The  immediacy  of  the  so-called 
immediate  inferences  is  psychological  not  logical. 

Objections  have  been  raised  to  all  such  extensions  of  Euler's 
diagrams.  These  criticisms  are  for  the  most  part  based  on  the 
existential  import  in  the  original  proposition.  It  has  been  main- 
tained by  Venn'  and  other  symbolic  logicians  that  the  two 
assumptions  that  we  have  made  concerning  the  original  propo- 
sition are  unwarranted.  The  proposition  from  which  we  start 
it  is  said,  tells  us  neither  (1)  that  S  and  P  exist,  nor  (2)  that 
non-S  and  non-P  exist.  But  I  think  this  is  not  a  serious  objec- 
tion. Any  explanation  of  immediate  or  mediate  inferences  is 
confronted  always  with  the  fact  of  a  multiple  hypothesis  con- 
cerning existence,  quantity  and  quality.  We  simply  contend  that 
the  operation  of  inference  here  involved  is  unconcerned  with 
these  hypotheses.  The  process  can  carry  along  several  hypo- 
theses as  well  as  one ;  it  accepts  what  is  given  it  and  passes  it 
along,  unchanged,  into  the  conclusion.  This  process  of  carrying 
along  a  multiple  hypothesis  we  shall  find  best  illustrated  in  the 
case  of  inversion — the  most  criticized  of  all  the  immediate  infer- 
ences. Yenn  has  objected  to  the  hypotheses  of  the  Eulerian  nota- 
tion because  they  are  very  remote  from  the  jiopular  view.  Formal 
Logic,  however,  should  not  concern  itself  with  the  popular  view, 
but  with  the  actual  facts.  All  teachers  of  the  subject  bear  testi- 
mony to  the  fact  that  elementary  students  accept  easily  the 
assumption  of  the  existence  of  ^S"  and  P  and  their  negatives ;  it  is 
the  assertion  that  one  or  more  of  these  classes  may  be  non-existent 
that  comes  as  a  surprise. 


3  Cf .  Venn,  Symbolic  Logic,  (ed.  2,  London,  Maemillan,  1894),  p.  154. 
"From  'All  X  is  Y'  we  are  commonly  allowed  to  derive  'All  not-Y  is 
Not-X. '  But  this  being  a  universal  affirmative  must  indicate  that  there 
are  instances  of  not-Y  and  not-X,  as  well  as  of  Y  and  X.  This  is  cer- 
tainly very  remote  from  the  popular  view,  which  never  thinks  of  insisting 
that'X  and  Y  must  not  only  exist  but  must  also  abstain  from  comprising 
all  existence. ' ' 


IMMhDI.lTE  INFERENCE  107 

II 

In  a  previous  chapter  we  saw  that  the  several  definitions  of 
inference  wliieh  were  examined  seemed  all  to  be  circular ;  nor  was 
our  own  definition  free  from  the  suspicion  of  a  return  to  itself. 
In  fact  we  aec('i)t('d  the  cii-cle  in  defining  as  ])y  no  means  a 
calamity.  There  are  no  ultimately  simple  units,  or  ])oints,  for 
thought.  It  begins  with  circles,  but  circles  whose  radii  are  zero, 
so  to  speak — whose  elements  are  concomitants,  not  sequents.  We 
shall  find  tlic  same  ditfieult}'  coiifi-outing  us  wlu-ii  now  we  come 
to  look  more  closely  into  the  miturc  of  the  so-callfM]  iiiiiiU'diate 
inferences. 

Every  proposition  has  a  meaning,  often  several ;  and  these 
meanings  have  meanings.  I  have  already  spoken  of  these  direct 
and  indirect  meanings  as  first  and  second  intensions  of  proposi- 
tions. I  employ  these  expressions,  first  and  .second  intensions,  in 
({uite  the  same  sense  as  the  scholastic  usage.  In  the  scholastic 
terminology,  the  first  intension  is  a  judgment  about  a  thing,  and 
the  second  intension  a  judgment  about  a  judgment.  Now  the  de- 
bated question  whether  the  immediate  inferences  of  ordinary'  logic 
are  real  inferences  or  just  interpretations,  transformations,  or 
to  use  another  suggestive  expression,  alternate  readings,  depends 
on  whether  we  can  establish  any  real  distinction  between  the 
first  and  second  intensions,  the  direct  and  the  indirect  meanings 
of  propositions.  The  defense  of  Formal  Logic  depends  ui)on  the 
validity  of  this  distinction.  If  the  second  intensions  are  wholly 
dependent  ui)on  the  first  intensions — if  they  have  no  domain 
within  which  they  uuiy  vary  independently  of  the  first  inten- 
sion— then  the  distinction  between  formal  reasoning  and  material 
reasoning  breaks  down.  However,  if  such  a  distinction  can  be 
made  out,  we  shall  be  able  to  say  that  any  movement  of  thought 
in  which  we  pass  merely  from  one  direct  meaning  to  another 
direct  meaning,  is  only  an  alternate  reading ;  whereas  if  thought 
passed  from  a  direct  to  an  indirect  meaning  we  should  have  a 
true  inference.     Perhaps  this  distinction  has  already  been  in 


108  FOOTNOTES  TO  FORMAL  LOGIC 

the  minds  of  those  authors  of  ekniientary  textbooks  wlio  have 
distinguished  between  implied  and  inferred  judgments.  But  I 
believe  the  distinction  in  kind,  upon  which  I  am  here  insisting, 
can  be  described  with  a  higher  degree  of  accuracy  by  the  terms 
direct  and  indirect  than  by  implied  and  inferred,  or  actual  and 
virtual.  I  have  already  tried  to  point  out  the  failure  of  all  those 
definitions  of  inference  which  rely  upon  the  pseudo-distinction 
between  the  old  and  the  neu\  or  that  attempt  to  describe  infer- 
ence as  progress  of  thought,  without  pointing  out  the  necessity 
of  both  identity  and  difference,  action  and  reaction,  in  short, 
genuine  reciprocity.  As  an  illustration  of  such  a  definition  I 
quote  from  Davis  :^ 

Au  imiilied  juilgnient  is  one  that  actually  exists  together  with  the 
given  judgment,  either  merely  in  thought  or  involved  covertly  in  the 
expression.  An  inferred  judgment  is  one  that  only  virtually  or  poten- 
tially exists  in  the  given  judgment,  and  is  derived  from  it.  The  statement 
of  the  one  is  nothing  new;  there  is  no  advance,  no  progress  of  thought, 
but  only  its  full  expression;  that  of  the  other  contains  something  new, 
there  is  a  step  forward,  a  progress  of  thought.  In  the  inferred  judgment 
there  is  always  either  a  different  subject,  or  a  different  predicate,  from 
that  of  the  premise,  and  perhaps  both. 

It  seems  unwise  to  use  the  terms  implied  and  inferred  to  describe 
the  different  moments  in  thought,  since  so  many  writers  on 
Symbolic  Logic  use  impliceition  and  inference  as  synonyms,  or 
nearly  so.  And  do  not  all  such  expressions  as  "step  forward" 
or  -'covertly  involved"  themselves  covertly  involve  the  whole 
problem  that  we  are  attempting  to  solve?  I  am  of  course  fully 
aware  that  the  terms,  first  and  second  intensions,  or  direct  and 
indirect  meanings,  are  by  no  means  free  from  the  objection  I 
have  raised  against  the  other  terminology. 

It  is  quite  impossible,  I  think,  to  distinguish  between  imme- 
diate and  mediate  inference  on  the  ground  of  a  numerical  differ- 
ence in  the  elements  involved  in  the  process.  This  is  the  most 
ancient  of  all  the  distinctions.  But  when  we  assert  that  in  an 
immediate  inference  the  conclusion  is  derived  from  one  premise 


i  Theory  of  Thought   (New  York,  Harper,  1878),  p.  103. 


IMMh.DIATK  IS Fi:i!i:S('E  lii9 

alone,  we  luivr  sultst  it  iili-d  one  (lirticully  U)V  aiiollit.'r.  The  vital 
point  at  issue  is  jiisi  the  i|iiesli()ii  as  lo  what  constitntos  one 
])i'()|)()sit  ion.  If  llie  fiiKiuss  of  IIm'  jiKh/nKiil  in  llic  mind  is 
always  to  be  found  in  the  oneness  of  the  spoken  or  pi-intecl 
proposiiion  then  Lojzfie  is  tiidy  just  another  nanu'  for  Grannnar. 
And  this  is,  in  fact,  wlial  some  pliilologists  claim.  Lof^ic,  tliey 
say,  beinj^-  eompelled  to  \vail  upon  hmguage,  is  eutii-ely  at  the 
nierey  of  tlie  aeeidents  of  sjjeeeh.  This  ol)viously  I'evives  the 
old  (piestion  so  ])i-oiuinent  in  the  wi'itings  of  Hamilton,  ]Mill, 
Manse!  and  Wlialely,  wheHiec  Logic  deals  witli  language,  thought 
or  things.  Here,  as  I  have  remarked  in  an  rar-Her  cliapler.  is 
where  the  doctrine  of  the  ciuantification  of  llie  predicate  luis  its 
strong  hold,  for  that  doctrine  is  precisely  such  a  scheme  for  filling 
out  the  sliort comings  of  language.  Were  it  not  foi-  the  inertia  of 
oui'  human  nature,  M'liich  in  language,  as  elsewhere,  follows  the 
line  of  least  resistance,  the  expression  of  thought  would  he  ade- 
quate to  thought  itself,  and  there  Avould  probably  he  no  such  thing 
as  inference.  When  one  goes  into  an  East  Side  restaurant  and 
hears  the  waiter  call  out  an  oi'der,  "Hot  cakes  and" — or,  "Ham 
and,'"  one  has  an  illustration  of  the  economy  of  language.  In 
the  mind  of  the  cook  in  tlie  adjoining  kitchen  one  would  find 
the  inference.  How'ever,  the  risk  is  taken,  we  economize  effort 
and  sa}j  less  than  we  fhinh.  But  we  pay  the  penalty  for  the 
indolence  of  language  in  tlie  perpetual  necessity  of  making_good 
the  omissions  by  the  process  that  we  call  inference.  All  efforts 
to  reduce  Logic  to  Grammar  have  their  origin  in  the  failui'e  to 
observe  this  distinction,  which  I  have  already  urged,  between 
the  interpretation  of  a  proposition  and  the  deduction  of  inf<  r- 
enccs  from  a  judgment. 

To  use  a  mathematical  metaphor,  which  T  admit  is  somewhat 
riskful,  we  may  say  that  there  is  both  a  one-dimensional  and 
two  dimensioiml  tlunight.  One  dimensional  thought  is  repre- 
sented by  the  Aristotelian  system  of  propositions  with  umiuanti- 
fied  pi-edicates.  Two-dimensional  thought  is  represented  in  the 
llamiltonian  system  of  propositions  with  (pnintitied  predicates. 


110  FOOTNOTES  TO  FOBMAL  LOGIC 

For  example,  in  the  universal  affirmative  proposition  "All  *S'  is 
P"  in  the  one-dimensional  system  of  thought  we  are  told  of  one 
relation  which  the  predicate  has.  In  this  system  when  the  predi- 
cate attaches  itself  to  the  subject  it  reserves  the  privilege  of 
other  attachments  with  which  S  is  not  concerned.  Situations 
might  arise  in  which  S  would  be  justified  in  knowing  P's  other 
attachments,  and  with  such  situations  only  the  system  of  propo- 
sitions with  quantified  predicates  would  be  competent  to  deal. 
If  we  regard  the  subject  in  extension  and  the  predicate  in  inten- 
sion, "All  8  is  P"  means  that  the  objects  in  the  class  *S'  all  have 
the  attribute  P;  but  the  proposition  does  not  tell  us,  and  we  have 
no  right  nor  need  to  know  whether  P  is  an  attribute  of  any 
other  object.  P  could  be  faithful  to  every  requirement  of  a 
({ualifier  of  8  and  qualify  other  objects  also.  The  question  as  to 
what  else,  if  anything,  P  does  qualify  is  a  perfectly  proper  ques- 
tion, but  this  lies  in  a  second  dimension  of  thought.  The  query 
arises  "where  or  what  is  Sf"  and  the  answer  is  "All  8  is  P." 
Then  a  second  query  arises  "where  or  what  is  F?"  This  is 
answered  by  the  Hamiltonian  A  or  TJ.  But  now  it  should  be 
noted  that  the  second  question  does  not  arise  simultaneously  with 
the  first ;  it  is  suggested  by  the  answer  to  the  first.  The  fact  that 
language  has  rarely  provided  the  Hamiltonian  forms,  shows 
clearly  that  the  one-dimensional  Aristotelian  forms  are  entirely 
adequate  to  the  first  questions.  Now  I  believe  this  distinction 
between  first  and  second  questions  has  an  important  bearing 
on  the  question  of  the  validity  of  immediate  inference.  An 
immediate  inference  always  involves  the  transition  from  the  one- 
dimensional  system  to  the  two-dimensional  system.  The  only 
genuine  inference,  therefore,  is  one  in  which  thought  passes 
from  a  categorical  to  a  problematic  proposition.^ 


5  Bradley,  Principles  of  Logic,  p.  390.  "The  truth  is  that,  if  you  keep 
to  categorical  affirmatives,  your  conversion  or  opposition  is  not  rational, 
but  is  simply  grammatical.  The  one  conversion  which  is  real  inference 
is  a  mortal  conversion,  and  that  presupposes  a  hypothetical  character 
in  the  original  judgment. ' ' 


IMMEDIATE  ISFKRENCE  111 


III 


As  we  liavc  a]rc;i(l\'  liad  IVcfiiifiil  occasion  to  I'cinark,  most 
definitions  say  that  an  inference  is  immediate,  not  because  it  is 
obvious  01-  direct,  or  is  grasped  in  a  single  beat  of  consciousness; 
it  is  inimeiliate  no  nuitter  how  many  so-called  steps  are  required 
to  reach  it,  ])rovided  no  otlier  information  is  used  than  what 
was  given  in  tlie  one  oi'iginal  proposition.  The  immediate  infer- 
ences have  been  so  denominat<'d  ])ecanse  thougiit  seems  to  pass 
froni  one  judgment  to  aiiotlu  r  witliout  the  assistance  of  a  middle 
term.  But  this  conventional  distinction  between  mediate  and 
immediate  inference  is  sadly  defective  in  fundamental  insight. 
A  common  ground  is  required  quite  as  much  in  immediate  as 
in  mediate'  inference,  as  a  means  of  bridging  the  gap  between 
the  two  judgments.  We  pass  from  one  particular  judgment 
to  another  particular  judgment  only  because  both  are  embedded 
in  a  universal.  All  thought  is  from  particular  to  particular  via 
the  univei'sal;  and  moreover  the  cei'tainty  and  value  of  the  con- 
clusion in  any  form  of  reasoning — immediate  or  mediate — 
depends  ui)on  the  grip  we  have  upon  the  universal. 

The  logician  therefore  has  to  contend  with  tliis  embarrassing 
fact  that  propositions,  as  men  use  them,  ai*e  not  always  univocal. 
It  is  this  ancient  question  of  the  precise  determination  of  what 
is  imj)lied  in  a  proi)osition,  and  what  is  extraneous  nuitter,  that 
is  the  cause  of  the  diffieulty  wliieli  so  many  recent  wi'iters  find 
in  these  transformations  of  })ropositions  which  have  now  so  long 
been  called  immediate  inferences.  It  is  evident  that,  when  one 
of  these  and)iguous  propositions  is  given  to  the  logician  to 
operate  ui)on.  lie  musT  insist  that  you  shall  announce  beforehand 
in  which  one  of  the  several  mt'anings  he  is  to  take  the  proposi- 
tion. However,  this  task  of  determining  the  precise  meanings 
of  propositions  belongs  to  the  per.son  who  announces  it — to  the 
rhetorician  or  granniiarian.  If  he  does  not  fix  the  meaning,  the 
logician  must  not  lie  blamed  for  drawing  his  inference  from  the 


112  FOOTNOTES  TO  FORMAL  LOGIC 

proposition  in  the  form  of  hypothetical  alternatives  correspond- 
ing to  the  alternatives  implied  in  the  original  proposition.  It 
sometimes  happens,  iiowever,  that  even  where  the  proposition 
from  which  we  start  seems  unambiguous  and  categorical  we  can 
not  infer  a  truth  equally  unambiguous  and  categorical.  This  is 
said  to  be  the  case  with  the  relation  which  has  commonly  been 
called  inversion.  The  inverse  may  be  defined  as  "a  proposition 
having  the  negative  of  the  original  proposition  for  its  subject 
and  the  original  predicate  for  its  predicate.'"''  The  inverse  of 
"All  S  is  F"  is  "Some  non-S  is  not  P."  The  inverse  has  also 
been  confused  with  the  contrapositive,  and  I  need  only  refer  to 
the  many  other  special  uses  of  the  word  in  algebra,  geometry, 
mechanics,  nuisic,  etc. 

The  opponents  "of  immediate  inference  have  attacked  inver- 
sion as,  in  their  opinion,  the  weakest  place  in  the  system  of  imme- 
diate inferences.  But  I  submit  that  no  logician  of  repute  has 
ever  claimed  universal  categorical  validity  for  the  process  of 
inversion.  Keynes,  who  was  the  first  to  give  a  thorough  treat- 
ment of  this  subject,  most  carefully  pointed  out  the  limits  of 
inversion.  He  says:  "It  is  indeed  quite  impossible  to  justify 
the  process  of  inversion  in  any  case  without  having  some  regard 
to  the  existential  interpretation  of  the  propositions  concerned.' 
Again,  Welton  says :  ' '  An  inverse  from  a  true  proposition  is 
not  necessarily  true  when  stated  categorically.  ...  It  is  thus 
seen  that  these  mediate  inferences  are  of  extremely  small  impor- 
tance ;  we  give  them  chiefly  for  the  sake  of  completeness.* 


G  The  word  inverse  is  employed  by  mathematicians  aud  logicians  in 
several  senses.  Professor  Eoyce  defines  the  inverse  as  follows:  "When- 
ever the  proposition  (a  E  b)  is  true,  there  is  always  also  a  relation,  often 
symbolized  by  E,  in  which  b  stands  to  a.  This  may  be  called  the  inverse 
relation  of  the  relation  E.  Thus  if:  "a  is  father  of  b,"  "b  is  child 
of  a";  and  if  one  hereby  means  "child  of  a  father"  the  relation  child  of 
is,  in  so  far,  the  inverse  of  the  relation  father  of."  Ency.  Philos.  Sci.,  I,  97. 

7  Keynes,  Studies  and  exercises  in  Formal  Logic  (ed.  4,  London,  Mac- 
millan,  1906),  p.  217. 

■^  Manual  of  Logic,  p.  305. 


IMMEDIATE  ISEEUESCE  li:; 

But  granted  that  inversion  is  a  process  that  often  yields  a 
hypothetical  conclusion — sometimes  even  doubly  conditional — 
this  does  not  destroy  the  pi-actical  valur  of  tliese  inferences.  It 
is  not  true  that  a  i)artial  liiith  is  no  tintli.  Tlie  }iy|)othetical 
conclusion  is  distinctly  "better  than  notliing. "'  All  languages 
are  full  of  "ifs, "  and  "if"  they  did  not  correspond  to  some- 
thing practical  and  also  something  theoretically  defensible  they 
would  have  been  elimiiuited  long  ago.  In  the  business  of  nar- 
rowing down  the  complexities  of  alternatives  which  we  meet 
everywhere  in  the  world  of  experience,  Ave  do  not  wait  until  we 
have  achieved  certainty.  In  our  seareli  for  truth  it  is  greatly 
worth  while  to  be  warned  away  from  error  by  the  destruction  of 
hypotheses  one  at  a  time.  This  we  saw  is  the  function  of  the 
infinite  judgment  whicli  some  logicians  hate  characterized  as 
meaningless  and  worthless. 

There  is  a  prevalent  delusion  among  the  enemies  of  tradition 
that  Formal  Logic  is  a  collection  of  rules  which  furnish  guid- 
ance of  a  positive  character  in  the  search  for  trutli.  But  not 
even  its  most  ardent  defenders  have  held  that  it  is  a  direct 
organon  of  knowledge.  It  is  primarily  by  warning  men  away 
from  error,  that  Formal  Logic  helps  them  in  their  efforts  to  reach 
truth.  In  deducing  the  inverse  the  logician  does  not,  as  has 
been  asserted,"  attempt  the  absurdity  of  proving  foxes  do  not 
hark  from  all  dogs  hark.  Now  in  the  first  place,  before  attempt- 
ing to  draw  any  of  the  innnediate  inferences  from  ^-1//  dogs  hark, 
we  must  remember  that  this  proposition  is  ambiguous,  or  to  be 
more  accurate,  it  is  brimful  of  suggestions,  meanings  and  impli- 
cations of  meanings.  It  is  in  short  a  ])ortmanteau  proposition. 
Tlie  logician  calls  upon  the  grammarian  to  fix  its  })uaii{)ig.  for 
not  until  then  can  he  determine  with  accuracy  the  implications 
or  inferences  from  the  meaning.  We  ask  this  proposition,  among 
others,  these  questions.  Do  dogs  exist:  Is  there  anything  that 
harks;  Are   tJure    hcings   other   tlia>i   dogs:   Is   iJiere   angtliing 


n  Cf.    L.    E.    Hicks,    iu    an    article    on    "Kulor's    circlos    and    adjacent 
space,"  Mind,  n.  s.  XXI  (1912),  413. 


114  FOOTNOTES  TO  FOBMAL  LOGIC 

that  docs  not  hark?  Also  we  may  inquire  (note  now  the  double 
query),  If  there  are  beings  other  tJian  dogs;  are  tJiere  any  of 
these  beings  that  do  not  bark;  also,  //  there  are  beings  that  bark 
and  if  some  of  these  are  not  dogs,  are  there  beings  that  are  not 
dogs  that  do  not  bark,  and  how  many.  It  is  evident  that  some  of 
these  are  questions  concerning  the  meanings  of  the  propositions 
and  some  are  questions  concerning  the  implications  of  the  mean- 
ings. Some  are  first  intensions  and  some  second  intensions. 
Among  the  former  there  is  obviously  the  question  of  the  existen- 
tial import  of  the  proposition.  The  logician  can  not,  indeed, 
peremptorily  demand  that  these  meanings  be  fixed,  but  he  can 
say  categorically  that  if  they  are  not  so  fixed  any  doubt  that 
remains  will  not  affect  the  process  of  inference  but  only  the 
conclusion.  The  inferential  process,  he  insists,  is  unerring;  it 
carries  along  unchanged  any  uncertainty  that  is  handed  to  it. 
Now  to  the  latter  question,  which  it  wall  be  observed  is  the 
inverse,  the  logician  replies,  Yes,  there  are  (on  these  conditions) 
some  beings  that  are  not  dogs  that  do  not  bark.  We  see,  then 
that  the  logician  merely  says  he  can  warn  you  away  from  error 
in  your  quest  for  an  animal  that  does  not  bark.  You  have 
been  told  that  all  dogs  bark  and  you  begin  your  search  for  an 
animal  that  does  not  bark,  w'hereupon  the  logician  tells  you 
categoriccdly  that  you  must  not  look  for  the  animal  that  does 
not  bark  among  dogs,  but  if  you  are  to  find  it  at  all  it  will  be 
somewhere  in  the  region  of  beings  that  are  not  dogs.  The  inver- 
sionist  is  prepared  to  treat  a  universal  negative  proposition  in 
a  like  manner,  although  there  is  greater  uncertainty  about  the 
meanings  of  the  original  proposition.  As  I  have  remarked,  he 
is  not  disturbed  by  the  existential  import  of  the  proposition.  It 
is  a  matter  of  common  observation  that  the  predicate  in  the  E 
proposition  need  not  exist  in  the  same  universe  as  the  subject. 
But  this  does  not  affect  the  process  of  inversion,  or  any  other  of 
the  immediate  inferences.  Such  restrictions  as  are  imposed  by 
the  existential  import  of  the  proposition  are  passed  on  intact 


/ .1/ .1/ /J)/ J  TE  INFERENCE  1 1 5 

into  the  conclusion.  We  are  challenged  to  find  the  inverse  of 
No  matlumatician  ran  square  the  circle  and  we  are  told  that 
to  do  so  we  must  pcfpct latc  llie  absurdity  of  inferring  from 
No  matlionatician  can  square  the  circle  that  Some  one  who  is 
not  a  mathematician  can  square  the  circle.  If  this  is  all  that  the 
process  accomplishes  it  would,  indeed,  he  "inversion  silliness." 
But  here  again,  tlic  real  function  of  inversion  is  to  warn  you 
away  fi-om  error.  Vou  set  out  in  search  of  some  one  to  scjuare 
the  circle.  Having  discovered  that  no  mathematician  can  per- 
form the  feat,  you  announce  this  to  the  inversionist,  who  there- 
upon replies,  "if  that  is  so  and  you  still  persist  in  your  search, 
I  can  tell  you  most  positively  that  if  you  are  to  find  anybody 
who  can  square  the  circle,  it  must  he  someone  among  those  who 
ar(  not  >n(ith(  niaticians."  No  inhabitants  of  Thessaly  ever  saw 
a  centaur.  The  categorical  inverse  of  this  proposition,  derived 
from  a  thrice-conditioned  premise,  would  read.  If  no  inhabitant 
of  Thessaly  ever  saw  a  centaur  and  if  am^body  ever  did,  it 
nuist  have  been  someone  wlio  was  not  an  inlia])itaiit  of  Thessaly, 
if  there  are  any  such.  Dr.  Mercier  disposes  of  the  inver.se  in 
his  customary  cavalier  fashion.     He  says  the  inverse 

...  is  arrived  at  by  a  method  so  complicated  that  T  will  not  trust  myself 
to  attempt  it,  but  will  take,  from  a  standard  textbook,  the  following 
example:  "Every  truthful  man  is  trusted" — Inverse,  "Some  untruthful 
men  are  not  trusted. ' '  Some  logicians  doubt  the  legitimacy  of  this  form 
of  Inference;  and  I  must  confess  to  misgivings  about  it;  for,  if  it  is 
valid,  I  see  no  reason  why  it  is  not  equally  valid  to  infer  from  ' '  Every 
truthful  man  is  mortal"  to  "Some  untruthful  men  are  not  mortal."  This 
puts  on  inveracity  a  premium,  which  is  scarcely  to  be  expected  from  the 
justice  of  Providence;  and,  what  is  more  to  the  purpose,  does  not  seem 
to  me  to  be  implied  in  the  postulate. lo 

Hut  a  valid  non-contradictory  inference  of  the  hypothetical  sort 
that  I  liave  desci'ibed  can  be  drawn  by  invei'sion  from  Dr. 
Mercier 's  example,  Every  truthful  man  is  mortal,  as  follows:  // 
every  truthful  man  is  mortal  then  if  there  are  any  beings  that 
are  not  mortal  they  will  be  some  of  those  beings  that  are  not 


loAV'H-  Logic,  p.  290. 


116  FOOTNOTES  TO  FOBMAL  LOGIC 

truthful  ]iieii.  And  this  is  an  inference  that  a  just  Providence, 
to  wlioni  Dr.  Mercier  appeals,  may  safely  accept. 

It  is  evident  that  the  process  of  inversion  is  adequate  to  any 
of  the  several  possible  situations  which  the  existential  import 
of  judgment  imposes.  Both  subject  and  predicate  and  their 
negatives  are  existent  in  the  same  universe  of  discourse.  This 
is  assumed  to  be  the  case  where  no  information  to  the  contrary 
is  furnished  the  logician  when  he  begins  his  task  of  inferring. 
If  any  other  meaning  is  intended  by  the  original  proposition  the 
logician  expects  to  be  informed,  for  example  (1)  that  neither 
subject  nor  predicate  exists,  (2)  that  one  exists  biit  not  the 
other,  (3)  that  either  subject  or  predicate  may  be  practically 
and  perhaps  theoretically  without  a  contradictory. 

Now  it  should  be  remarked  that  we  are  not  here  concerned 
with  the  question  whether  this  conclusion  is  a  "new"  truth; 
that  is  a  question  which  concerns  the  whole  class  of  so-called 
immediate  inferences.  Nor  should  we  object  seriously  if  some 
one  should  maintain  that  this  process  of  inversion  is  neither  an 
immediate  nor  a  mediate  inference  as  those  operations  are  com- 
monly defined.  There  is  a  striking  resemblance  between  inver- 
sion, when  it  is  expanded  into  a  form  that  exhibits  all  of  its 
parts,  and  that  one  of  Russell's  "ten  axioms''  of  Symbolic  Logic 
which  he  has  called  the  Principle  of  Importation.  "The  prin- 
ciple states  that  if  2^  implies  that  q  implies  r,  then  r  follows  from 
the  joint  assertion  of  p  and  q.  For  example:  "If  I  call  on 
so-and-so,  then  if  she  is  at  home  I  shall  be  admitted"  implies 
"  If  I  call  on  so-and-so  and  she  is  at  home,  I  shall  be  admitted. '  '^^ 

IV 

The  criticisms  of  inversion  which  I  have  attempted  to  answer 
all  rest  back  upon  an  alleged  failure  to  regard  the  existential 
import    of    propositions.      Another    objection    has    been    raised, 


11  Principles  of  Mathematics,  p.  16. 


IM MEDIA  IK  IXFKL'KXCE  1 1 7 

namely,  thai  the  process  involves  an  illicit  distribution.  In  "All 
S  is  /-•/'  J*  is  undistril)uted  while  in  tiie  inverse  "Some  non-S 
is  not  /'."  I'  has  become  distributed.  I  think  there  is  here  a 
serious  misunderstanding  as  to  the  meaning  of  distribution.  The 
medieval  law  concerning  distribution  stated  that  no  term  must  be 
distributed  in  the  converse  if  it  was  not  distributed  in  the  con- 
vcrtend.  But  now  it  should  l)e  ol)served  that  this  law  was 
intended  only  to  apply  to  conversion,  where  the  prior  require- 
ment had  been  imposed,  namely,  that  the  quality  of  the  proposi- 
tion must  not  be  changed.  However,  in  the  obverse,  retroverse, 
contraverse,  inverse,  the  quality  of  the  proposition  has  suffered 
a  change  in  passing  to  the  inference ;  and  here  a  different  inter- 
pretation of  distribution  is  icciuind.  The  distribution  of  terms 
in  negative  propositions  does  not  mean  the  same  thing  as  the 
distribution  in  the  affirmative  proposition.  The  failure  to 
recognize  this  fact,  has  brought  confusion  into  discussions  con- 
cerning the  validity  of  inversion,  as  we  shall  see  presently.  A 
term  is  said  to  be  distributed  when  Ave  know  something  about 
every  member  of  the  class  designated  by  the  term.  In  the  propo- 
sition *'A11  S  is  P,"  8  is  distributed  because  we  know  something 
about  every  member  of  the  class  8,  namely,  that  it  is  a  P. 

But  in  the  E  proposition,  ''No  8  is  P."  while  we  nmy  say 
again  that  .S^  is  distributed  because  we  know  something  about 
every  member  of  the  class,  this  knowledge  is  of  a  different  kind 
from  what  we  had  in  the  case  of  the  A  proposition.  In  ''Xo  8 
is  P,"  I  know  something  about  every  .S'.  namely  that  it  is  not  a  P, 
and  this  I  know  indirectly.  This  indirect  process,  when  made 
explicit  is  as  follows :  first  and  most  fundamentally  I  know 
that  " 8  is  not  'non-8"  and  then  because  P  happens  to  be  some- 
where in  the  region  of  non-8  (though  I  am  quite  ignorant  of 
just  where  it  is)  I  know  that  "8  is  not  P."  We  met  this  diffi- 
culty in  the  chapter  on  the  infinite  judgment.  We  saw  that 
negation  is  always  a  degree  more  remote  from  reality  than 
affirmation.     Every  significant   negation,  when  fully  expanded 


118  FOOTNOTES  TO  FOEMAL  LOGIC 

reads:  Since  P  is  in  the  region  of  non-S,  and  since  *S'  excludes 
non-iS  it  excludes  that  which  is  included  in  non-S,  namely  P. 

But  now,  referring  to  the  diagram  for  the  universal  affirma- 
tive proposition  on  page  it  would  seem  that  if  P  is  undis- 
tributed, non-P  should  likewise  be  undistributed.  This  non-dis- 
tribution of  P  we  have  represented  in  the  diagram  by  the  dotted 
lines,  indicating  that  the  class  P  is  undefined.  So  far  as  S  is 
concerned,  P  might  widen  its  sphere  of  application  as  far  as  it 
pleased,  even  to  the  extent  of  pushing  non-P  off  the  map  of 
existence.  However,  if  this  dotted  line  marks  the  boundary 
between  the  two  classes  P  and  non-P,  it  would  seem  that  non-P 
should  have  the  same  indefinite  range  as  P.  But  we  have  not 
told  the  whole  truth  about  the  circle  P  when  we  have  said  that 
its  expansion  ouiward  is  unlimited,  we  must  observe  that  its 
contraction  inward  is  definitely  limited.  It  is  this  lower  limit 
wliich  the  very  nature  of  the  universal  affirmative  proposition 
permits  us  to  disregard,  that  in  turn  becomes  an  upper  limit  for 
the  expanding  class  non-P.  Non-P  may  expand  only  to  the 
limit  to  which  P  may  contract.  This  anomalous  fact  is  exhibited 
also  in  the  process  of  obversion.  In  "All  S  is  P,"  P  is  undis- 
tributed, but  in  its  equivalent  ''No  N'  is  non-P,"  the  non-P  is 
distributed. 

But  this  apparent  contradiction  in  the  medieval  law  of  dis- 
tribution when  it  was  applied  beyond  conversion,  did  not  attract 
the  attention  of  logicians  until  the  process  of  inversion  was 
reached.  Now  although  the  difficulty  has  become  more  acute 
in  the  case  of  inversion,  it  is  nevertheless  in  my  opinion,  precisely 
the  same  difficulty  that  has  just  been  pointed  out.  Keynes 
noticed  this  difficulty  in  the  apparent  violation  of  the  Law  of 
Distribution  and  gave  an  explanation  of  it  that  has  been  followed 
by  Creighton  and  others. 

It  will  be  remembered  that  we  are  at  present  working  on  the  assump- 
tion that  each  class  represented  by  a  simple  term  exists  in  the  universe 
of  discourse,  while  at  the  same  time  it  does  not  exhaust  that  universe; 


IMMI.niATF.   ISI'EUESCE  119 

iu  otluT  won  Is,  we  assume  tliat  !i,  not-S,  not- 1',  all  represent  existing 
classes.  This  assumption  is  perhaps  specially  important  in  the  case  of 
inversion,  and  it  is  connected  with  certain  difficulties  that  may  have 
already  occurred  to  the  reader.  In  passing  from  AH  S  is  P  to  its  inverse 
Some  not-S  is  not  P  there  is  an  apparent  illicit  process,  which  it  is  not 
quite  easy  either  to  account  for  or  explain  away.  For  the  term  P,  which 
is  undistributed  in  the  premiss,  is  distributed  in  the  conclusion,  and  yet 
if  the  uni\orsal  validity  of  obversion  and  conversion  is  granted,  it  is 
impossible  to  detect  any  flaw  in  the  argument  by  which  the  conclusion 
is  reached.  It  is  in  the  assumption  of  the  existence  of  the  contradictory 
of  the  original  predicate  that  an  explanation  of  the  apparent  anomaly 
may  be  found.  That  assumption  may  be  expressed  in  the  form  Some 
things  are  not  P.  The  conclusion  Some  not-S  is  not  P  may  accordingly  be 
regarded  as  based  on  this  premiss  combined  with  the  explicit  premiss. 
All  S  is  P,  and  it  will  be  observed  that,  in  the  additional  premise  P 
is   distributed. 12 

IJiit  now  this  is  merely  an  elucidation  of  the  difficulty  not 
an  explanation  of  it.  The  time  explanation  is  to  be  found  in  the 
double  meaning  of  distribution.  Each  term  in  a  proposition,  as 
we  have  just  stated,  has  an  upper  and  a  lower  limit  to  its  exten- 
sion. Our  attention  need  l)e  directed  towards  only  one  of  these 
limits,  the  other  is  ignored.  For  i)raetieal  purposes  we  may  say 
that  we  do  have  some  genuine  knowledge  even  if  our  class  is 
bounded  merely  on  one  side.  But  for  the  purposes  of  exact 
thinking  both  the  upper  and  lower  limits  must  be  observed,  and 
this  is  what  the  doctrine  of  the  (|uantitication  of  the  predicate 
attempted  to  accomplish.  The  inverse  of  the  affirmative  proposi- 
tion "All  S  is  P"  is  as  Keynes  has  said,  "Some  non-S,  is  not  P." 
It  is  indeed  one  and  the  same  class  P  that  is  considered  first  with 
S  and  then  with  non-S  as  subject.  But  in  the  one  case  we  see 
P  on  its  bounded  or  limited  side  and  in  the  other  the  unlimited 
side.  There  is  no  contradiction,  according  to  our  point  of  view, 
in  asserting  that  P  is  both  distributed  and  undistributed.  The 
quantification  of  the  predicate  is  a  device  for  looking  at  P 
from  both  sides  at  once. 


12  Formal  Logic,  p.  189. 


120  FOOTNOTES  TO  FORMAL  LOGIC 

V 

The  theor.y  of  inference  which  I  have  proposed  in  these  pages, 
namely,  that  every  true  inference  must  mark  a  transition  from 
a  categorical  to  a  modal  proposition,  removes  some  of  the  diffi- 
culties about  the  particular  proposition.  It  is  evident  that,  since 
the  true  particular  is  always  a  modal  assertion  the  passage  to 
such  a  particular  is  always  a  true  inference.  The  particular 
judgment  is  always  a  problematic  judgment  in  disguise.  "Some 
aS?  is  P'Ms  equivalent  to  " S  may  be  P."  Venn,  and  other  sym- 
bolic logicians  after  him,  have  defined  some  as  not  none.  This 
is  quite  in  agreement  with  one  side  of  the  popular  meaning  of 
the  word.  This  definition  provides  an  unambiguous  relation  of 
some  to  its  lower  limit  none,  but  there  is  still  an  ambiguity  in  its 
relation  to  the  upper  limit,  all.  It  may  include  or  exclude  all. 
This  latter  ambiguity,  the  popular  mind  also  aims  to  avoid  and 
so  prefers  the  interpretation  of  some  as  not  all,  as  well  as  not 
none. 

Some  is  a  variable  moving  toward  a  limit  in  two  directions, 
but  in  different  senses.  In  the  downward  direction  toward  none 
it  can  not  reach  its  limit,  while  in  the  upward  direction  toward 
all  it  may  reach  the  limit.  The  particular  proposition  of  ordi- 
nary logic  on  this  view,  is  semi-indefinite,  being  defined  by  its 
exclusion  of  none  and  yet  undefined  by  its  inclusion  of  all.  There 
are  thtis  seen  to  be,  theoretically  at  least,  four  possible  relations 
between  some  and  its  limiting  classes:  (1)  Some  includes  none 
and  all,  or  (2)  it  excludes  them  both,  or  (3)  it  includes  the  all 
and  excludes  none,  or  (4)  it  includes  none  and  excludes  all. 
Some  has  been  identified  with  the  indeterminate  class  of  Symbolic 
Logic.  This  is,  I  think  a  mischievous  error.  The  some  of  Tra- 
ditional Logic  has  never,  even  its  most  liberal  interpretation 
included  more  than  two  of  the  four  possible  relations  between  the 
indeterminate  class  and  its  limiting  classes,  none  and  all. 

Every  such  discussion  of  the  meaning  of  some  that  intends  to 


IMMEDIATE  IXEEIiENCE  121 

define  it  in  terms  oi"  either  its  limits,  all  and  nonr,  presupposes 
that  thes<'  limits  themselves  have  already  been  defined,  lint  jiow 
we  should  find  it  difficult  to  define  none  in  any  other  way  than 
by  reference  to  sonic,  and  if  )ionc  implies  some,  we  move  in  a 
vicious  circle  in  defining  sonic  as  not  none.  We  have  here 
another  illustration  of  what  has  so  often  been  pointed  out  in  the 
recent  discussions,  especially  those  in([uiries  into  the  nature  of 
the  fundanu'iilal  concepts  of  nuithematics,  that  when  we  deal 
with  ultimate  concepts  it  is  impossible  to  avoid  the  circle  in 
defining. 

It  has  been  alleged  that  tlie  particular  proposition  has  for  its 
collateral  aim — if  not  its  distinctive  i)urpose — to  a.ssert  that 
objects  I'eferi'ed  to  by  the  subject  do  exist.  When,  for  example, 
I  say,  "Some  California  Poi)pies  are  scarlet,"  my  primary  pur- 
pose is  to  assert  the  existence  of  such  flowers  and  secondarih' 
only  am  I  concerned  to  give  the  information  that  their  color  is 
scarlet.  It  is  evident  that  the  prinuiry  function  of  the  particular 
proposition  is  in  reality  what  ai)pears  to  be  merely  its  secondary 
or  indirect  function.  Tiie  particular  affiruuitive  proposition, 
"Some  S  is  P,"  taken  at  its  face  value,  means  to  affirm,  but  in 
practice  its  intentions  is  to  deny  tlie  universal  negative.  Like- 
wise, the  })articular  negative  is  employed  to  deny  the  universal 
affirmative.  This  latter  fact  is  disclosed  by  the  form  which  the 
particular  negative  so  often  takes  in  all  languages,  "  All  N  is  not 
F,"  "Not  All  S  is  P."  These  forms,  which  perplex  the  student  of 
elementary  logic,  are  only  rightly  understood  when  the  purpose 
to  overthrow  the  universal  is  considered. 


CHAPTER  VII 

THE  CASE  AGAINST  THE  SYLLOGISM 

I 

The  syllogism  has  always  been  attacked  on  two  scores.  It  is 
alleged,  in  the  first  place,  that  it  is  structurally  defective — it 
begs  the  ciuestion.  Secondly,  it  is  held  that  it  is  not  universally 
applicable.  Mill  criticized  the  syllogism  on  the  former  count 
and  Bradley  on  the  latter.  In  view  of  the  various  attacks,  both 
upon  the  validity  and  the  universality  of  the  syllogism  since  Mill, 
and  more  particularly  in  view  of  the  recent  developments  of 
Symbolic  Logic  the  Aristotelian  account  of  the  subject  demands 
a  new  interpretation.  Aristotle  defined  syllogism  as  "discourse 
in  which  certain  things  being  posited,  something  else  than  what 
is  posited  necessarily  follows  merely  from  them."  This  defini- 
tion contains  five  words  each  of  which  to  say  the  least,  is  moder- 
ately ambiguous.  Before  the  exact  scope  of  this  definition  can 
be  understood  we  must  know  (1)  the  nature  of  the  "things 
posited";  (2)  what  we  mean  by  "positing"  or  "laying  down"; 

(3)  in  w^hat  the  difference  of  the  "something  other"  consists; 

(4)  and  what  is  meant  by  "following,"  especially   (5)   "neces- 
sarily following"? 

We  may  ask  two  questions  concerning  Aristotle's  own  account 
of  the  syllogism.  First,  what  precisely  did  he  himself  mean  by 
the  definition,  as  sliown  by  the  context.  Secondly,  granted  that 
Aristotle's  own  discussion  of  the  syllogism  left  certain  forms  of 
thought  outstanding,  is  it  possible  to  give  a  wider  interpretation 
to  the  several  words  of  his  definition  than  he  himself  gave,  so  that 
the  so-called  asyllogistic  types  of  reasoning  may  be  encompassed 
by  it  ?    If  we  give  to  each  of  these  five  elements  of  the  definition 

[  122  J 


THE  CASE  AdAIXST  THE  SV Ll.Od lS.]f  ]23 

its  most  lihcral  iiilci'|)i'c1;it  ion,  I  l)clic\c  it  ciin  \if  sliowii  tliat  tlie 
case  af^ainst  the  s\iIo<i:isiii  is  not  so  (laiiia<;iii'j:  as  tlie  New  Logic 
believes. 

Tlie  ordinary  aeeoiait  of  the  syllogism  as  incdiat*'  iiii'erenee 
is  unsatisfactory  because  it  is  too  vague.  The  difficulty  of  dis- 
tinguishing between  the  immediate  and  the  mediate  in  thought, 
I  have  dwelt  upon  elsewhere.  So,  too,  the  description  of  the 
syllogistic  j)roct'ss  as  a  comparison  of  concepts  lacks  in  explicit- 
ness.  Again,  Sidgwick,  wlio  differs  from  the  othci'  opponents  of 
Formal  Logic  in  his  belief  that  the  syllogism  is  the  universal 
form  of  thought,  proposes  a  definition  which  has  a  number  of 
ill-defined  terms.  "A  syllogism  may  thus  be  regarded  as  con- 
sisting of  three  parts:  tlie  rule  ("major  premiss")  ;  the  identi- 
fication of  a  case  as  coming  under  it  ("minor  premiss")  ;  and 
the  conclusion  inferred  as  a  result  of  applying  the  rule  to  the 
case.  "^  If  we  interpret  each  of  the  words  in  the  Aristotelian 
definition  li])erall>',  I  think  it  can  be  shown  tliat  the  syllogism  is 
the  universal  foi-m  of  thought.  In  its  widest  possible  meaning 
it  will  be  found  always  to  consist  in  tlir  correlation  of  genus, 
species,  particular ;  or  universal,  particular,  singular.  I  believe 
that  every  thought,  l)e  it  true  or  false,  will  conform  to  this  con- 
ception of  syllogism.  It  is  impossible  to  think  otherwise  than 
in  this  form.  It  is  hardly  necessary  to  say  that  this  interi)i-eta- 
tion  of  the  syllogism  is  meaningless,  or  at  least  is  ])lainly  open 
to  the  two  criticisms  of  lack  of  universality  and  begging  the 
question,  if  the  relation  between  particular  and  species,  and 
species  and  genus  is  taken  in  pure  extension.  These  relations 
are  sui  generis;  they  are  not  to  be  confused  with  numerical  or 
quantitative  relations  as  ordinarily  understood.  The  relation 
of  pai'tieular  to  speci(»s  is  not  the  indifferent  relation  of  the  one 
to  the  many,  nor  is  the  I'elation  of  species  to  genus  the  merely 
associative  relation  of  ])art  to  whole.  The  relation  is  vital  and 
reciprocal.     This  relation  mi^'lit  be  expresseil  as  universal,  par- 


1  Ehmnitarn  Logic,  p.  "I'll. 


124  FOOTNOTES  TO  FORMAL  LOGIC 

ticiilar,  individual;  but  we  should  avoid  this  designation,  because 
the  term  individual  is  highly  ambiguous  in  philosophy.  In  the 
nomenclature  of  Logic  singular  is  preferable  to  individual.  We 
should  notice  also  that  the  term  particular  is  ambiguous.  For 
in  the  threefold  designation,  genius,  species,  particular,  and 
universal,  particular,  singular,  the  word  particular  in  the  latter 
series  corresponds  to  species  in  the  former.  But  this  ambiguity 
in  the  use  of  particular  is  in  our  common  speech  as  well.  We 
say,  "Give  me  the  particulars  of  this  affair";  and  again,  "What 
particular  sort  of  flower  do  you  mean?"  However,  this  am- 
biguity is  not  so  important  as  in  the  case  of  individual.  The 
latter  is  a  difference  in  kind,  the  former  simply  a  difference  in 
degree.  Individual  usually  means  a  single  case.  When  I  ask 
"What  particular  individual  occupies  that  seat?"  I  mean  to 
identify  or  to  designate  some  particular  one.  But  the  word  is 
likewise  used  in  an  entirely  different  sense,  as  when  one  says, 
"I  like  individuality."  By  this  w^e  mean  the  singular  plus  the 
evidences  of  self-activity.  In  this  sense  individual  stands  for 
spontaneity,  life,  growth.  An  individual  is  a  fountain  of  ever- 
increasing  newness  and  originality.  This  latter  use  of  individual 
is  not  pertinent  to  Formal  Logic,  where  a  stick  or  stone  is  as 
good  an  individual  as  a  soul.  Thinking  is  always  viewing  in  the 
light  of  genus,  species,  particular,  or  considering  the  relation  of 
universal,  particular,  singular.  "I  think,"  means  that  I  see 
this  particular  in  the  light  of  that  species,  and  the  species  in  the 
light  of  the  genus,  or  else  that  I  am  carrying  on  the  reverse 
process,  seeing  the  whole  or  genus,  and  taking  under  it  the 
species,  and  seeing  the  particular  as  under  the  species.  Both 
the  rigid  syllogism  of  deduction  and  the  un-rigid  syllogism  of 
induction  are  consistencies,  and  must  be  explained  in  terms  of  the 
threefold  relation,   genus,  species,   particular.-      Syllogizing,   or 


2  This  view  of  pan-syllogism  I  owe  to  the  lectures  of  Professor  Howi- 
son.  An  interpretation  very  like  this  has  been  given  by  Mr.  Joseph, 
although  he  denies  its  universality.  He  says:  "The  central  idea  of 
syllogism   is   that   it   works   through   concepts,   or   universals.      The   major 


Till':  CASE  ACAISST  TTl K  SYLLOGISM  12G 

thinking  tog(4h('f,  tliereforo,  always  involves  classification.  We 
can  think  iiiwai'dly  i'roiii  tlic  wliulc,  1hroii^''li  the  members,  to 
the  minntcst  iiicnibei-s ;  or  outwardly  from  llu-  iiiiinitest  member, 
to  the  larger  member,  then  to  the  class,  and  to  the  largest  class. 
I  am  not  unmindt'ul  ol'  wiiat  I  am  eonnnitted  1o  in  llie  assertion 
that  all  thinking  is  syllogistic  and  that  this  always  implies  classi- 
fication. Symbolic  Logic  has  shown  that  thfe  definition  of  a  class 
is  the  most  imi)oi'taiit  and  ditficult  of  all  the  prol)lems  of  Logic. 
We  may  eomli  nm  1lie  class  view  of  predication,  but  we  cannot 
escape  from  the  fundamental  fact  of  comparison  that  lies  some- 
where at  the  heart  of  all  judgment  and  all  judgment  about  judg- 
ment. It  may  be,  as  Russell  and  McColl  have  asserted,  that 
propositions  are  more  fundamental  than  classes;  this  would  not, 
however,  ai¥ect  the  theory  of  pan-syllogism.  Thought  is  a 
"relating  activity";  from  this  there  seems  no  escape.  But  an 
analysis  of  any  act  of  comparison  or  the  definition  of  relation 
I'eveals  a  number  of  difficulties.  We  cannot  compare  on  the  one 
hand  total  identities  nor  on  the  other  hand  complete  disparates. 
Sameness  without  dift'erence  or  difference  without  sameness  makes 
comparison,  judgment,  or  classification  impossible. 

This  syllogistic  process  is  distinct  from  that  of  just  perceiv- 
ing with  the  senses.  The  perceptive  judgment  is  different  from 
the  cognitive  judgment — the  former  is  not  a  stage  on  the  way  to 
the  latter.  We  do  not  classify  when  we  see,  or  hear,  or  smell, 
that  is  to  say  we  do  not  correlate,  or  see  in  a  higher  unity.  In 
sense  as  such  we  do  not  have  unity,  only  separateness.  We  may 
have  a  pseudo-unity  in  the  association  of  sensations.  Thought 
is  the  process  of  unification  in  which  we  harmonize  so  as  not  to 
obliterate  the  items.  We  retain  their  distinctness  and  discover 
the  harmony  between  them.  Or  again,  thought  is  a  unifying 
process,  by  which  we  retain  the  clearness  of  each  part  in  obtain- 
ing the  whole.     ^Moreover,  the  two  processes  of  unification  and 


premiss  asserts,  not  the  presence  of  ^  in  every  B  (and  therefore  in  C, 
among  them),  but  the  connection  of  A  as  such  with  B  as  such:  hence 
wherever  we  find  B,  wo  must    find  A."     Introduction  to  Lofiic,  p.  28-i. 


126  FOOTNOTES  TO  FOBMAL  LOGIC 

separation  vary  inversely,  paradoxical  as  it  may  seem.  The  more 
firmly  the  integrating  power  clutches  the  items  the  more  clearly 
does  the  separating  actively  differentiate  them.  All  this  is  appro- 
priately expressed  in  the  name  syllogism  and  M'ithout  doing 
violence  to  its  etymology  or  to  Aristotle's  own  conception  of  its 
scope. 

I  have  already  referred  to  the  other  aspects  of  this  syllogistic 
fact  Avhich  we  need  to  notice  before  we  can  obtain  a  complete 
view.  We  still  find  the  statement  in  textbooks  that  besides  this 
one  form,  there  are  two  others;  that  the  syllogism  is  only  one  of 
three  forms  of  thought,  namely:  (1)  conceptions  or  notions,  (2) 
judgments,  (3)  the  syllogism.  The  impression  is  still  too  often 
left  with  the  student  that  we  first  have  conceptions,  and  that  we 
then  pass  on  to  the  combination  of  these  in  judgment,  and  finally 
to  the  higher  form  in  which  three  judgments  are  connected  in  a 
syllogism.  Any  such  mechanical  or  corpuscular  theory  of  thought 
is  faulty.  Thought  is  not  a  mere  aggregation  of  symbols  of 
thought.  The  nature  of  thought  is  to  produce  its  own  elements; 
it  creates  hoth  itself,  and  its  memhers.  Thought  is  a  whole,  so 
whole  that  it  furnishes  to  itself  its  own  members  and  also  com- 
bines them.  The  reciprocal  process  of  determining  the  whole 
into  its  elements  and  the  elements  into  the  whole,  constitutes  the 
fundamental  distinction  of  deduction  and  induction — the  rigid 
and  the  un-rigid  syllogism. 

But  hereupon  it  may  justly  be  asked  Avhere  do  we  get  the 
distinction  between  the  relation,  conception,  judgment  and 
reason,  and  the  relation  genus,  species  and  individual?  To  this 
query  we  can  only  reply  that  both  relations  are  fundamental, 
unanalyzable  and  indefinable.  We  just  think  our  thoughts,  and 
cannot  but  think  them.  Every  conscious  experience  that  we  call 
thought  must  stand  the  light  of  a  syllogism,  else  it  is  not  a  real 
experience.  If  we  cannot  think,  that  is,  syllogize  our  experience, 
we  do  not  have  any.  As  to  the  series,  concept,  judgment, 
syllogism,  we  cannot  get  along  M'ithout  these  names,  but  the 


THE  CASE  AGAINST  THE  SYLLOGISM  lL'7 

syllogism  is  not  the  last  result  or  j)rocluct  from  the  union  of 
judgments,  that  were  tlieniselves  the  products  of  concepts.  The 
eonce])t  is  not  tlie  ultimate  element  of  tiiought;  on  the  contrary 
the  tiiought  unit  is  the  syllogism  itself. 

The  syllogism  is  the  omnipresent,  all-embracing  form,  defined 
as  the  thought  that  casts  itself  in  the  correlated  distinction  of 
particular,  species,  genus,  or  universal,  particular,  singular. 
These  three  distinctions  each  depend  for  their  meaning  on  the 
correlation  of  tlif  three.  A  significant,  "just  this"  always  pro- 
vokes the  query  "just  this  what?"  Hence  it  is  necessary  to  tell 
the  species.  Someone  says  to  me,  "I  want  you  to  see  this";  I 
immediately  ask,  "this  what?"  Now  if  I  really  do  see  it,  it  is 
this  or  that  or  the  other  ol)ject  that  I  see.  It  has  correlation 
(shape,  size,  color,  etc.),  and  through  this  correlation  it  is  con- 
nected with  the  species.  In  looking  for  the  tJiis,  we  see  the  color 
or  the  shape,  and  so  we  connect  it  directly  with  species.  If  w-e 
did  not  take  in  the  others  of  the  species  we  would  not  see  the 
tltis.  The  singular  means  nothing  except  in  the  light  of  the 
particular,  and  the  particular  means  nothing  except  in  the  light 
of  tlie  universal.  All  ])('reeption,  all  intelligence,  is  knowing  in 
the  light  of  the  whole.  Conversely,  the  whole  means  nothing 
without  the  final  this.  Without  the  descending  steps  in  the  cor- 
related things,  it  is  not  a  whole,  it  is  nothing.  The  universal 
without  the  species  and  the  genus,  is  an  abstraction,  is  nothing. 
The  abstract  singular  and  the  abstract  universal  are  alike  noth- 
ing. Hence  a  thing  that  does  not  contain  its  own  differentia  does 
not  exist. 

The  syllogism  cannot  i)roceed  without  liaving  j)arts  and  a 
whole  upon  which  to  operate.  Parts  that  are  just  parts — that 
have  no  relation  to  any  whole,  have  no  meaning.  They  are  parts 
of  nothing  and  so  are  themselves  nothings  about  which  nothing 
can  be  asserted.  Furthermore  no  judgment  is  ever  just  the  sum 
of  units  that  existed  prior  to  the  whole  which  they  constitute. 
The  quantitative  whole  which  seems  to  be  composed   of  units 


128  FOOTNOTES  TO  FORMAL  LOGIC 

qualitatively  alike  is  no  exception.  This  is  reached  by  a  process 
of  abstraction  in  which  the  parts,  having  become  qualitatively 
indifferent  to  each  other,  have  also  sacrificed  their  unique  rela- 
tions to  the  whole.  The  whole  is  thus  lost  to  sight  when  it  is  no 
longer  required  as  the  synthesis  of  the  different  and  differing 
facts.  But  no  whole,  not  even  the  abstract  quantitative  whole, 
may  disappear  entirely.  Quantity  is  just  the  latent  device  for 
holding  asunder  parts  which  are  qualitatively  alike.  This  thought 
I  shall  develop  further  presently. 

The  singular  is  not  made  up  out  of  the  universal,  nor  the  uni- 
versal out  of  the  singular,  nor  the  particular  out  of  either. 
Neither  can  we  start  with  the  all  (which  is  an  empty  name  when 
taken  alone)  and  from  it  arrive  at  the  particular,  and  so  pass 
on  to  the  singular.  For  this  is  equivalent  to  starting  with  noth- 
ing, and  trying  to  make  of  it  a  lower  class,  and  of  this  in  turn 
still  a  lower  class,  the  final  result  will  still  be  nothing.  We  cannot 
think  these  things  apart ;  without  the  particular  and  the  singular, 
the  whole  is  nothing,  they  are  all  intrinsically  correlated,  and  are 
not  to  be  taken  apart.  The  syllogism  is  not  a  composite,  nor  an 
analysis  of  a  composite,  but  an  individual  whole  furnishing 
intrinsically  its  own  elements.  Thus  it  is  clear  that  no  one  of 
the  three  forms  of  thought  sets  out  with  one  unanalyzable  ele- 
ment. "We  do  not  begin,  as  the  empirical  theory  of  association 
would  have  us  begin,  with  thought  atoms,  then  proceed  with 
combinations  of  these.  The  syllogism  is  a  harmonic  unity,  a 
unity  of  correlated  elements  existing  intrinsically  in  correlation. 
The  syllogism  in  this  sense,  we  repeat  with  insistent  emphasis, 
is  the  cardinal  fact  wherever  there  is  a  thought ;  it  is  the  universal 
type  of  thought. 

II 

It  is  however,  insufficient  to  say  that  the  syllogism  is  the  uni- 
versal form  of  thought,  differentiating  itself  into  the  syllogism 
as  concept,  the  syllogism  as  judgment,  and  the  syllogism  as  argu- 


THE  ('.isf:  ja.irxsT  riir:  sv lux. ism  129 

iiit'iil,  or  1li;it  it  is  II1C  iiiii\rrs;il,  oimiiprcsciil  I'oi-ui  of  thought, 
the  indivisible,  corivlatecl  unity  embracing  universal,  particular 
and  singular.  We  must  show  how  and  why  this  correlation 
appears  in  three  different  ways.  There  is  need  in  short  of  dis- 
tinguishing between  the  im})licit  and  IIh'  <x|)Iicit  presence  of  the 
syllogism.  In  the  concept,  the  syllogism  is  only  implicitly  pre- 
sent. To  bring  the  implication  out  in  the  clearest  way,  it  is 
necessary  to  show,  as  we  have  in  part  already  shown,  that  judg- 
ment is  implied  in  tlie  concept.  It  is  so  implied,  since  the  con- 
cept means  nothing  unless  it  is  a  whole,  ensphering  a  great  many 
marks,  or  implicit  judgments.  And  it  has  therefore  rightly  been 
said  tliiit  in  judgment,  we  explicate  the  corresponding  concept, 
which  is  the  subject  of  the  judgment.  In  the  judgment  we  say 
that  the  concept  is  so  and  so.  If  I  assert  that  I  have  a  concep- 
tion, and  T  am  asked  what  my  conception  is,  T  answer  by  making 
a  series  of  judgments.  For  example,  I  am  asked,  "What  is  a 
salanuuider?"  I  reply,  "It  is  a  reptile,  it  is  scaly,  it  can  stay 
in  the  fire  without  being  burnt,  etc."  Here  I  am  explicating  the 
concept,  salamander,  by  making  a  number  of  judgments  bring- 
ing out  th"  various  characteristics  of  the  salamander,  in  each  of 
which  judgments  I  employ  a  predicate  and  connect  it  with  the 
concept  by  a  copula.  The  concept  (as  a  thought)  is  therefore  an 
implicit  bundle  of  judgments.  So,  also  it  may  be  shown  that 
every  judgment  is  an  implicit  syllogism.  Suppose  that  I  assert 
"X  is  Y."  You  ask,  "What  is  it  to  be  Y?"  I  answer  ''Y  is  Z." 
Then  of  course  "A'  is  Z."  The  filling  out  of  the  recjuired  mean- 
ing of  tlie  judgment  makes  us  go  on  and  complete  the  s.yllogism. 
We  can  continue  in  this  way  indefinitely,  until  we  come  to  a 
predicate  beyond  which  we  cannot  go.  This  implied  process  in 
thought  is  seeking  the  real  whole,  from  which  each  part  takes  its 
significance. 

Every  thought  implies  two  elements  and  their  union  in  a 
third.  All  reasoning  is  from  particular  to  particular  via  the 
universal.    This  uniting  act  Formal  Logic  has  always  preferred 


130  FOOTNOTES  TO  FOEMAL  LOGIC 

to  call  the  coj^ula.  The  word  is  appropriate,  yet  in  one  sense 
quite  inappropriate,  for  copula  really  means  a  link  or  yoke,  and 
suggests  an  artificial  union ;  we  are  apt  to  think  of  it  as  uniting 
two  distinct  things.  But  the  elements  united  in  thought  are  not 
two  distinct  things.  The  truth  is,  the  syllogism  is  an  indivisible, 
complex,  unitary  act,  and  the  copula  furnishes  the  principle 
which  both  joins  and  separates  the  parts  of  the  whole.  It  is  the 
function  of  the  copula  to  "couple  apart."  Bosanquet  writes: 
"In  analysing  the  judgment  as  an  act  of  thought  we  may  begin 
by  dismissing  the  separate  coupla. ""  To  this  we  may  yield  a 
hearty  assent,  but  there  is  no  good  reason  why  the  word  itself 
should  not  be  retained  to  designate  the  real  act  involved  in  the 
synthesis  of  subject  and  predicate.  The  copula  is  the  inner  activ- 
ity that  permeates  each  of  the  two  parts  and  grips  them  into 
a  whole.  Two  pieces  of  magnetized  iron  that  cohere  are  a  better 
illustration  of  the  function  of  the  copula  than  the  link  between 
two  cars.  In  the  case  of  the  two  pieces  of  iron,  every  molecule 
in  each  piece  takes  part  in  the  enwholing  grip.  In  terms  of  this 
act  of  joining  through  the  copula,  we  can  determine  the  distinc- 
tion between  the  concept,  the  judgment,  and  the  syllogism.  The 
difference  between  these  three  is  a  difference  in  the  degree  of 
explication  of  the  copula.  In  the  concept,  the  copula  is  not 
explicit  at  all,  but  implicit.  In  the  judgment,  the  copula  is 
explicit,  but  appears  simple,  as  though  on  the  surface,  having  no 
complexity.  In  the  syllogism,  the  complexity  of  the  copula  comes 
entirely  into  light. 

It  is  not  only  convenient,  but  necessary  for  the  purposes  of 
exposition  and  communication  of  thought,  to  adhere  to  the  dis- 
tinction between  dynamic  and  static  relations  and  to  say  that 
the  syllogism  is  competent  to  deal  only  with  the  latter.  This  is, 
however,  a  distinction  that  has  to  do  with  "thought  expressed"; 
it  does  not  concern  "thought  in  reality."  Such  a  distinction 
blinks  at  the  real  difficultv.     The  dvnamic  relations  themselves 


3  Essentials  of  Logic,  p.  99. 


THE  CASI-:  ACAISST  Till-.  SV LI.OC, I s.\l  i:jl 

cannot  exist,  oi'  at  least  caiinot  he  tlioii^'-lit,  without  a  iiuivei'sal 
witliin  wliicli  the  apparently  int  faiisit  i\-e  relations  are  enclosed. 
Now  tliei'e  are  in  realit>  no  piii-el\'  intransitive  relations.  Even 
in  tlie  temporal  series  the  pieseiit  harks  liaek  to  the  past — the 
effect  in  a  sense  causes  the  cause.  Vet  the  (lyiunnic  order  and 
the  static  order  have  something  in  conunon,  and  it  is  tiie  task 
of  Logic  to  discover  this  pervading  ejeinent.  It  is,  of  course 
true  that  any  reasoning  which  explains  phenomena  through 
causes  is  not  syllogistic  in  the  naiTower  interpfetat  ion.  lint 
when  we  take  the  larger  view  o!"  .syllogism  as  thought  exliil)iting 
itself  in  the  threefold  relation  of  singnlai',  parliculai'  and  uni- 
versal; or  pai't  ieulai',  sjjecies  and  genus,  we  find  tliat  reasoning 
through  causal  determination  is  no  exception  to  its  scope. 

("onunon  sense  reads  class  relationships  in  one  direction  only. 
It  supposes  that  in  any  series  of  more  and  more  inclusive  groups 
the  stahility  of  the  smaller  group  nuist  give  way  if  it  interferes 
with  the  stability  of  the  larger.  The  part  is  suboi'dinate  to  the 
whole.  This  seems  an  elemental  truth.  But  the  discernment  of 
this  truth  as  an  axiomatic  principle  is  a  far  simpler  matter  than 
its  practical  application.  In  what  does  the  stability  of  any  group 
consist,  and  what  constitutes  interference  with  the  stability  of  a 
larger  group,  and  what  precisely  constitutes  a  larger  and  a 
smaller  group?  Merely  a  cursory  examination  of  group  rela- 
tions reveals  the  hidden  truth  that  some  aspects  may  always  be 
found  in  which  the  smaller  includes  the  larger.  In  extension  the 
species  is  included  in  the  genus,  but  in  intension  the  genus  is 
included  in  the  species.  The  principle  of  total  one-way  inclusion 
seems  a  chimera.  There  ai)pear  to  be  no  groups  such  that  the  one 
is  in  every  way  included  within  the  other.  Real  groups  involve 
only  transitive  and  symmetrical  relations.  The  relation  between 
a  so-called  small  group  and  its  including  larger  group  must  ever 
exhibit  the  fundamental  relation  between  part  and  whole,  in 
which,  as  we  have  seen,  the  parts  and  the  whole  are  equally  real ; 
each  includes  and  is  included  by  the  other.    Neither  presupposes 


132  FOOTNOTES  TO  FOEMAL  LOGIC 

the  other,  nor  is  either  more  real  than  the  other.  Neither  has  a 
stability  to  which  the  other  owes,  in  every  way,  unquestioned 
allegiance.  Such  a  view  of  class  relations  will,  I  believe,  go  far 
toward  vindicating  the  universality  of  the  syllogism. 

The  most  difficult  and,  I  believe,  the  most  important  of  all  the 
problems  of  Logic  is  the  relation  of  extension  to  intension.  Upon 
this  distinction  depend  the  vital  questions  of  the  meaning  of 
class,  the  import  of  judgment,  the  fundamental  metaphysical 
question  of  the  relation  of  quantity  to  quality,  and  above  all  the 
question  of  the  validity  and  universality  of  the  syllogism.  The 
elementary  textbooks  find  little  difficulty  with  this  subject  for 
there  is  a  superficial  definition  of  these  words  that  makes  this 
relation  simple  and  comprehensible  enough.  Some  writers  have 
been  aware  of  the  difficulty  of  defining  each  of  these  words  in  a 
way  that  would  make  their  relation  in  one  object  intelligible. 
Jevons,  for  example,  says  "I  believe  that  the  reader  who  once 
acquires  a  thorough  apprehension  of  the  difference  of  these  mean- 
ings, and  learns  to  bear  it  always  in  mind,  will  experience  but 
little  further  difficulty  in  the  study  of  Logic."*  However, 
Jevons'  own  treatment  of  the  subject  is  most  nai've  and  ignores 
entirely  the  real  issue,  namely,  the  essential  incommensurability 
of  the  extensive  and  the  intensive  series.  Aristotle  taught  that 
the  extensive  and  the  intensive  modes  of  predication  were,  at 
bottom,  equivalent  and  the  question  of  priority  meaningless.  He 
declares  most  explicitly  that  there  is  no  difference  between  saying 
that  one  thing  is  entirely  included  in  another  and  saying  that 
the  other  thing  is  always  a  predicate  of  the  one.^  ]\Iathematics, 
until  very  recent  times,  has  always  glorified  quantity,  and  the 
older  symbolic  logicians  taught  that  the  point  of  view  of  extension 
was  so  fundamental  in  all  our  thinking  that  intension  might  be 
entirely  disregarded.  The  philosophers,  on  the  other  hand, 
insisted  on  the  primacy  of  quality,  and  declared  that  the  relation 


*  Elementary  Lessons  in  Logic  (New  York,  Macmillan,  1914),  p. 
•'"'  C.f.  Prior  Analytics,  I. 


THE  CASE  AGAIXST  THE  SYLLOCISM  l.'J.'J 

between  subject  and  predicate  was  distorted  from  truth  in  the 
extensive  intcrjjretaticjn  of  jndf^iiient.  Mill  and  many  writers 
since  have  insisted  that  tlie  intension  of  terms  must  be  taken  as 
both  psychologically  and  logically  i)rimary,  and  extension  as 
secondary.  ^lill,  to  be  sure,  held  that  some  terms  have  no  conno- 
tation, but  only  denotation,  and  that  such  terms  always  denoted 
the  subject  directly  and  connoted  its  attributes  indirectly.  But 
this  was  the  interpretation  of  the  relation  for  the  purpo.se  of 
communication.  Mill  himself  plainly  implied  that  in  fhoiiglit 
connotation  is  primary;  but  since  we  rarely  have  the  qualities 
in  a  sufficiently  definite  and  tangible  grasp,  we  resort  to  the 
denotation  in  defining  or  describing  the  object.  A  familiar  illus- 
tration of  this  is  found  in  ordinary  intercourse  where  we  often 
find  it  more  convenient  to  describe  an  object  by  telling  whrre 
it  is  tlian  icJint  it  is.  But  in  all  these  debates  concerning  the 
meaning  of  extension  and  intension  and  the  nature  of  their 
relation,  the  contestants  never  suspected  that  there  might  be 
intermediate  positions  between  extension  and  intension ;  or,  that 
since  a  good  case  could  be  made  out  for  the  priority  of  each, 
perhaps  neither  was  fundamental  but  that  both  were  correlated 
aspects  of  a  more  fundamental  point  of  view. 

The  first  difficulty  that  the  naive  treatment  of  the  relation 
of  connotation  to  denotation  met  was  the  obvious  fact  that  the 
law  of  inverse  variation  was  not  universally  applicable.  It  is  not 
strictly  accurate  to  say  that  as  the  extension  increases  the  inten- 
sion decreases  and  vice  versa.  In  the  calculus  of  classes  where  the 
distinction  between  subject  and  predicate  is  effaced  and  the  con- 
tent of  proposition  represented  diagrammatically  as  by  Euler 
and  Venn,  this  may  be  j)artly  true.  However,  it  is  not  a  faithful 
account  of  the  psychological  process  involved.  The  ])ower  of 
thought  to  widen  its  field  of  attention  is  not  incompatible  with  a 
simultaneous  deepening  of  its  intensive  insight.  It  is  a  conunon 
practical  occurrence  and  one  that  has  a  deep-seated  theoretical 
justification,   that,    in   extending   its   synthetic   grasp   over   new 


134  FOOTNOTES  TO  FOBMAL  LOGIC 

instances,  thought  is  continually  discovering  attributes  hitherto 
latent.  In  considering  the  subject  of  analysis  and  synthesis  in 
judgment,  and  the  correlated  question  of  novelty  and  sameness, 
I  attempted  to  point  out  how  essential  it  was  to  any  right  under- 
standing of  the  import  of  judgment  to  see  that  the  synthetic 
and  the  analytic  functions  of  thought  may  both  operate  each  in 
its  own  opposite  direction.  No  antinomy  is  involved  in  describ- 
ing certain  systems  as  exhibiting  simultaneously  integration  and 
differentiation. 

The  relation  of  extension  to  intension,  of  quantity  to  quality 
is  of  such  vital  importance  that  I  wish  to  pursue  this  matter  still 
farther  even  at  the  risk  of  indulging  in  subtleties  that  may  appear 
to  the  reader  quite  out  of  place  in  the  present  discussion  of  the 
nature  and  validity  of  the  syllogism.  No  idea,  which  is  in  the 
least  extended — that  is,  no  quantitative  idea  can  be  brought  into 
consciousness  by  one  indivisible  act.  Any  single  pulsation  of 
consciousness  does  yield  size,  that  is  Gestalt-Qiialitat  or  form, 
just  as  it  does  quality ;  but  such  a  simple  act  of  consciousness  can- 
not give  us  the  notion  of  extension  regarded  as  a  system  of.  inter- 
related parts.  The  notion  of  true  quantity  never  comes  to  us 
in  a  single  beat  of  consciousness.  It  is  a  continuous  manifold, 
and  yet  a  manifold  which,  though  never  grasped  by  one  indivi- 
sible act  of  mind,  is  on  the  other  hand  equally  incapable  of  being 
produced  by  a  mere  repetition  of  units,  or  ultimate,  simple  ele- 
ments. We  have  here,  again,  the  perennial  problem  of  the  rela- 
tion of  the  part  to  the  whole,  of  individual  to  species,  of  a  term 
to  the  class  of  which  it  is  a  member.  This  problem  is  so  closely 
connected  with  the  question  of  the  relation  of  quantity  to  quality, 
that  we  may  partially  solve  the  difficulty,  I  think,  if  we  examine 
it  where  it  appears  in  another  form,  namely,  in  the  relation  of 
the  arithmetical  to  the  geometrical  continuum. 

]\Iodern  mathematics  has  discovered  that  the  arithmetical 
and  the  geometrical  continuum  are  different  facts,  both  for 
description  and  explanation.     We  never  pass  directly  from  one 


TUE  CASK  AUAIXST  THE  SILJJJGIS.M  Urj 

to  the  other  either  in  praetice  or  in  theory.  The  geometrical 
continuum  resists  any  attempt  numerically  to  exhaust  its  mean- 
ing; and  the  arithiiu-tieal  eontiinnim  can  never  be  regarih.'d  as 
the  first  step  in  the  logical  process  of  the  development  of  the 
geometrical  continuum.  All  such  attempts  to  derive  one  con- 
tinuum from  the  other  are  vicious  circles.  When  we  respond  to 
the  demand  for  an  absolutely  single  and  simple  element,  Ave  find 
that  the  spatial  continuum,  which  is  quantity  or  extension  par 
excellence,  presents  insupei'able  difficulties  to  conceptual  analysis. 
The  mathematician  responds  to  this  challenge  to  find  ultimate 
elements  by  declaring,  "Thei-e  are  points."  But,  when  required 
to  define  tlicse  ])oinls,  ln'  finds  that  they  are  .just  the  self-con- 
tradictory outcome  of  this  search  for  the  ultimate  elements.  This 
definition  is  self-contradictory  for  the  reason  that  when  the 
m;itli('iii;itician  reverses  the  process,  he  discovers  that  he  cannot 
get  back  from  his  points  to  the  contiiuumi  from  which  he  started. 
No  repetition  of  the  point,  as  such,  can  give  rise  to  the  line,  that 
is,  not  the  continuous  or  quantitative  aspect  of  the  line.  We  have 
here  the  familiar  paradox  concerning  the  discrete  and  the  con- 
tinuous aspects  of  quantity.  Because  of  its  incapacity  to  pene- 
trate things  to  the  bottom  of  their  real  natures  an  imperfect 
mind  must  resort  to  a  quantification  of  them.  Let  me  illustrate: 
0  and  ()'  lire  two  objects  wliich  are  ([ualitatively  alike  differing 
only  in  ([uantity,  that  is,  they  are  members  of  a  lowest  species. 
Thought  first  contemplates  the  object  0  by  itself.  It  discovers 
that  i1  is  uiial)ie  to  penetrate  the  object  to  the  core  of  its  mean- 
ing. A  certain  opacity  prevents  the  finite  mind  from  ever  reach- 
ing the  essential,  individual  nature  of  0.  But  0  is  not  yet  a 
quantity,  for  ([uantity  is  never  the  content  of  such  a  single  pul- 
sation of  consciousness.  BafUled  in  its  attempt  to  discover  the 
true  nature  of  0  by  internal  searching,  thought  seeks  for  that 
desired  information  from  an  external  source.  It  betakes  itself 
to  the  other  of  0,  or  0',  which  is,  howevei-,  in  itself  just  as 
impenetrable  for  thought  as  O  was.     0  and  ()'  are  conceptually 


136  FOOTNOTES  TO  FOEMAL  LOGIC 

alike,  and  yet  the  mind  perceives  a  difference  between  them. 
Every  attempt  to  explain  this  difference  lands  lis  in  an  inevitable 
contradiction. 

But  now  in  this  second  pulsation  of  consciousness  the  quanti- 
tative aspect  of  0  and  0'  has  suddenly  appeared.  Quantity  is 
that  mysterious  somewhat  that  can  not  be  found  in  either  0  or  0' 
when  contemplated  alone  but  does  somehow  seem  to  exist  in 
each  when  both  are  viewed  together.  Quantification  might  then 
be  described  as  the  result  of  our  finite  efforts  to  discover  exter- 
nally the  inaccessible  internal  meanings  of  things.  Or  I  might 
say  it  is  the  search  for  a  mediator  between  objects  where  the  com- 
plete understanding  of  each  is  by  the  very  nature  of  things 
impossible. 

Herein  lies  also  the  solution  of  the  apparent  contradictions 
in  the  discreteness  and  the  continuity  of  quantity.  The  dis- 
creteness arises  from  the  necessary  duality  of  the  thought  pro- 
cess that  produces  the  quantitative  way  of  viewing  things.  The 
continuity  is  simply  the  compulsion  under  which  thought  lies  of 
holding  the  two  objects  0  and  0'  in  a  unitary  grasp  of  conscious- 
ness in  order  to  explain  the  unfathomable  mystery  of  each.  From 
the  absolute  point  of  view  0  and  0'  of  our  illustration,  instead 
of  being  covered  by  one  concept,  are  provided  each  with  a  con- 
cept of  its  own  which  is  adequate  to  its  essential  nature.  A 
perfect  mind  has  no  need  to  view  things  under  the  category  of 
quantity.  For  finite  thought  quantity  is  simply  the  ever  present 
reminder  of  the  irrationality  of  sense.  Finite  thought  is,  once 
for  all,  inadequate  to  sense.  Every  tltis  that  it  contemplates  is  a 
this  only  in  appearance.  To  our  limited  minds  the  tliis  reveals 
only  its  thisness.  But,  as  I  have  already  pointed  out,  the  thisness 
of  the  this  contains  as  a  part  of  its  meaning  a  reference  to  a  that. 
And  now  comes  the  crucial  point.  Finite  thought  feels  itself 
irresistibly  impelled  to  search  for  the  that  to  which  the  this 
points,  which  in  reality  it  must  mean  to  be  a  this.  The  mind 
at  once  discovers  that  it  has  entered  upon  a  hopeless,  an  unending 


•/•///■;  cish  .if;.u.\sr  riiE  svi.i.fxiisM  1.37 

task;  for,  no  sooner  do  wc*  discovei-  llic  lliut,  which  we  liad  lioped 
would  solve  the  inexplieal)le  mystery  that  enshrouds  the  tliis, 
lliaii  it  turns  out  to  he  not  ;i  Ihal  at  all,  hut  the  identical  Ihis 
from  which  oui-  thouf^ht  started,  'riiouji^lit  has  in  a  fashion,  to  he 
sui'e,  solved  the  puzzle;  hut  in  the  solution  it  has  likewise  rein- 
stated its  original  question.  Here  we  find  an  explanation  not 
onl\'  I'oi'  the  disei'cteness  of  extension  and  its  contiiniity,  hut  also 
for  its  infinitude.  The  process  descrihed  is  evidently  of  the 
reeuri-ent  type,  hut  I  think  it  dilfers  in  one  essential  feature  from 
the  K(U(  that  Pi-ofessor  Koyce  has  so  often  described.  In  the 
present  Kcttc,  the  process  is  in  the  end  a  tautological  one.  Each 
new  member  of  the  Kette  has  novelty  only  so  long  as  it  is  con- 
templated as  a  fact  still  external  to  the  series,  that  is,  as  the  goal 
towai'd  which  each  individual  pulsation  of  thought  strives  for 
the  mouu^nt.  But  as  soon  as  the  goal  is  readied — when  once  that 
new  link  has  been  welded  into  connection  with  the  rest — the 
novelty  it  formerly  possessed  vanishes  into  an  inevitable  same- 
ness with  the  whole.  The  novelty  is  only  a  transitory  aspect  of 
the  essential  tautology  in  the  process.  The  novelty  is  accountable 
for  the  discreteness  of  extension,  the  tautology  for  its  continuity. 

Ill 

If  the  .syllogism  is  merely  an  expr(>ssion  of  the  relation  of 
classes,  where  each  class  is  taken  in  extension  only,  that  is,  where 
the  thought  is  uni-directional,  it  will  truly  not  compass  all  the 
forms  in  v.liicli  we  may  reason.  Such  class  reasoning  always  con- 
foruis  to  the  following  type:  (1)  the  uuijor  preuuse  is  an  enum- 
erative,  universal  pi-oi)ositiou  in  which  we  afhrm  that  each  .1/ 
is  seen  (by  actual  observation)  to  ))e  in  the  class  /'.-  and  (2)  the 
minor  premise  states  that  N  is  ()l)scived  to  be  one  of  these  M's; 
then  (3)  the  conclusion,  N  will  be  in  class  P.  This  view  of  the 
syllogism  has  rightly  been  condemned,  firstly,  because  of  its 
evident  tautology  and  secondly,  because  it  is  not  uni\-crsall\- 
applicable.      The   fii-st    of   these   ci-iticisms,    lunnel.w    that    it    is   a 


138  FOOTNOTES  TO  FOEMAL  LOGIC 

pctitio  appeared  long  before  Mill's  classic  assault.  It  was 
advanced  frequently  by  Aristotle 's  own  students.  The  second  of 
the  criticisms  is  very  j^revalent  in  recent  discussions.  As  has 
now  so  often  been  pointed  out  by  Bradley,  and  others,  there  are 
many  forms  of  inference,  for  example,  those  that  are  concerned 
with  dynamic  relations,  in  which  there  are  no  class  relationships, 
or  in  which  we  are  not  conscious  of  any  such  relations.  I  think, 
however,  that  all  such  relations  can  be  compassed  by  the  class 
relations  when  they  are  given  the  interpretation  I  have  offered. 
It  is  an  unwarranted  limitation  of  the  scope  of  the  syllogism 
to  restrict  its  application  to  the  old  class  view  of  judgment. 
There  is  no  mention  of  classes,  that  is,  classes  in  extension,  in 
Aristotle's  definition  of  the  syllogism:  "Syllogism  is  discourse 
in  which  from  certain  things  laid  down  other,  different  things 
follow."  The  things  "laid  down"  in  the  major  premise  are  not 
"laid  down"  according  to  any  j^rinciple  of  inclusion  or  exclu- 
sion. Aristotle  was  obliged  to  distinguish  (as  every  logician 
must)  between  thought  and  language.  In  the  actual  thought 
process  the  relation  of  an  individual  to  a  class  was  for  Aristotle 
always  a  relation  in  intension.  But  when  this  intensive  relation 
Avas  translated  by  him  into  a  form  available  for  exposition  and 
communication  it  took  the  inevitable  form  of  a  relation  in  exten- 
sion. The  charge  of  a  petitio  can  not  be  brought  against  the 
present  pan-syllogism.  It  employs  the  true  universal  which  is 
an  assertion  about  things  before  they  have  been  experienced, 
and  which  is  in  a  sense,  therefore,  always  hypothetical.  Now 
since  the  major  premise  is  hypothetical,  and  the  conclusion  is 
categorical,  it  is  impossible  that  the  latter  could  have  been  con- 
tained in  the  former.  Moreover,  when  it  is  said  that  the  conclu- 
sion contains  "new"  knowledge,  it  is  not  knowledge  that  is 
totally  disconnected  from  the  premises ;  for  no  process  of  infer- 
ence, mediate  or  immediate  can  ever  deliver  such  new  knowledge. 
It  is  new  knowledge  in  the  sense  that  it  is  then  for  the  first  time 
ohset'ved. 


THE  CASE  AGAINST  TEE  SYLLOGISM  V.'.O 

There  is  abmidaiil  evidence  cvcrywlu'i-e  in  Aristotle's  treat- 
ment of  the  subject  that  he  was  fully  aware  of  the  two  kinds  of 
universal  propositions — the  abstract  or  pseudo-universal  which 
is  a  collection  of  actually  observed  particulars,  and  the  true  or 
concrete  universal,  which  (by  asserting  a  connection  of  attri- 
butes) refers  not  1o  any  definite  group  of  individuals,  but  to  an 
entirely  indefinite  group.  The  pseudo-universal,  "All  aS'  is  P," 
means,  "Each  S  (and  I  have  examined  and  counted  them)  is  a 
P."  The  true  universal  "All  8  is  P,"  means  ";S'  as  such  is  P,  or 
if  S  then  P.  The  question  whether  the  syllogism  in  its  applica- 
tion of  the  dictum  cle  omni  et  nulla  involves  a  petitio  as  I  have 
said  hinges  on  the  sense  in  wliieli  we  take  the  major  premise.  If 
this  is  construed  as  an  liistorical  or  enumerative  judgment,  then 
manifestly  the  conclusion  is  just  one  of  the  particulars  which 
has  gone  into  the  aggregate,  bound  together  by  the  all  in  the 
major  premise.  The  so-called  universal,  that  is,  the  enumerative 
or  historical  universal  is  itself  merely  an  aggregate  of  particular 
truths  and  has  no  greater  validity  than  the  particulars  which 
constitute  it — it  is  itself  another  particular.  Aristotle  pointed 
out,  and  it  was  an  insight  that  always  seemed  irrefutably  clear 
to  him,  that  the  universal  nature  of  an  object  could  never  be 
reached  by  examining  and  counting  particular  instances. 

But  even  in  a  syllogism,  where  the  major  premise  is  a  pseudo- 
universal,  just  an  aggregate  of  observed  individuals,  there  is 
often  a  movement  in  thought,  in  which  there  is  novelty  in  the 
conclusion.  The  major  premise  although  strictly  an  enumerative 
universal,  does  not  contain  the  conclusion  nor  even  predict  it. 
The  two  premises  have  come  to  us  by  different  routes  and  it  is 
only  in  the  combination  of  the  two  that  the  conclusion  is  reached. 
For  example,  if  a  num  sliould  learn  from  the  telegraphic  reports 
that  the  entire  Second  Regiment  were  taken  prisoners  in  the 
battle  of  the  Marne,  and  tlien  on  consulting  the  lists  in  the  War 
Office  should  find  that  his  son  was  enlisted  in  this  Second  Regi- 
ment, the  conclusion  that  his  son  was  captured  is  something  over 
and  above  the  agony  of  suspense  that  came  from  the  unsupported 


140  FOOTNOTES  TO  FOBMAL  LOGIC 

major  premise.  To  the  authorities  in  the  War  Office,  who  have 
before  them  at  one  time,  botli  the  telegraphic  report  and  the 
record  of  enlistments,  there  is  not  the  novelty  in  the  conclusion 
that  there  is  for  the  anxious  parent. 

In  the  perfect  mind  premises  and  conclusions  are  concomit- 
ants not  sequent s,  and  hence  all  reasoning  in  such  a  mind  would 
involve  an  essential  tautology.  But  for  the  purpose  of  com- 
municating its  intuitive  knowledge  to  minds  on  lower  levels  of 
insight  the  perfect  mind  would  employ  the  syllogism  and  the 
accusation  of  tautology  would  be  unjustified.  On  this  view,  then, 
the  syllogism  is  the  instrument  of  communication  between 
minds  having  different  degrees  of  insight  into  the  relations  among 
things.  The  perfect  mind  would  not  syllogize,  nor  would  imper- 
fect minds,  if  tliey  all  had  simultaneously  the  same  degree  of 
knowledge  of  facts. 

Bradley  has  condemned  the  syllogism  at  times  with  vitriolic 
vocabulary.  The  mildest  of  the  epithets  that  he  has  applied  to 
it  is  "a  chimera."  And  yet  he  often  comes  quite  near  to  con- 
ceding all  that  its  defenders  have  thought  w^orth  contending  for. 
He  sa^'s:  "If  it  were  admitted,  on  one  side,  that  the  syllogism 
supplies  no  general  type  of  the  reasoning  act,  it  might  be  allowed, 
on  the  other  side,  that  it  is  a  mode  of  stating  the  principle  which 
is  used  in  that  act.  It  is  universal  as  a  form  for  showing  the 
explicit  and  conscious  exercise  of  a  function.''  This  is  an  admis- 
sion both  of  a  form  and  of  its  universality.  The  formalists  have 
never  claimed  for  any  of  the  forms  of  thought  an  existence  prior 
to  and  separated  from  its  concrete  setting.  They  have  granted 
freely  that  there  are  no  antecedent  types  or  schemes  for  thought. 
The  form  of  thought  as  we  have  shown  in  an  earlier  chapter 
is  a  vital  constructive  principle  within  the  so-called  object  matter 
of  thought  itself.  There  is  some  thing  in  every  concrete  act  of 
thought  that  always  detaches  itself  from  the  thought,  something, 
as  Bradley  himself  has  said,  that  is  "more  abstract  than  the 
argument  itself." 

"  Principles  of  Logic,  p.  482. 


THE  CASE  AGAINST  THE  SYLLOCISM  141 

IV 

It  may  not  be  evident  to  tlie  rciuU'i-  liow  nmch  tlie  fore^oin^ 
discussion  owes  to  Kant's  well-known  defense  of  the  s.\llojrisiii. 
The  logical  doctrine  of  iinirLs  tnii^lil  hy  l\;iiil  li;is  had  coiitiMnpt 
heaped  upon  it,  particularly  by  Hh!gel,  wlio  holds  it  i-esponsible 
for  much  of  the  confusion  in  the  discussion  of  the  nature  of  im- 
mediate and  mediate  inference.  Hegel  said  :  "There  is  no  more 
striking  mark  of  the  toniialisin  ami  drca\'  of  logic  llian  ihe 
favorite  category  of  Ihe  iiiark."  ""  Kant's  account  of  the  doc- 
trine has,  T  venture  to  think,  bei'U  much  misunderstood  and 
maligned.  It  will  he  I'cmembered  that  he  defined  judgment  as 
the  coiiiiiai'ison  of  a  thing  with  some  nuirh,  and  ratiociiiatio)i  as 
a  judgment  by  means  of  a  nu'diate  attribute.  And,  the  supreme 
rule  of  all  ratiocination  he  stated  thus:  "A  mark  of  a  mark  is 
a  mark  of  a  thing  itself."    Nota  noiae  est  nota  rei  ipsiiis. 

The  criticism  that  Kant  did  not  prove  his  dictum  deserves 
only  passing  attention.  It  would  not  be  the  highest  or  final 
rule  if  it  were  capable  of  i)roof.  Any  attempt  to  prove  the 
supreme  formula  of  all  raliociiuition  would  l)e  to  reason  in  a 
circle.  Proof  would  be  possible  only  by  means  of  one  or  more 
inferences.  This  principle  claims  to  be  the  final  anchorage  of 
all  certaint>'  in  reasoning  and  can  no  more  be  challenged  than 
the  indemonstrable  propositions  of  Symbolic  Logic.  The  two 
criticisms  which  Josej)!!'  has  urged  against  Kant's  principle  are 
more  pertinent.  However,  neither  of  his  objections  appears  to 
me  a  serious  indictment.  The  first  is  that  the  rule  assumes  the 
minor  term  is  always  a  concrete  thing.  Kant  would  have 
admitted,  I  tliink,  that  this  was  precisely  his  intention  and  would 
not  have  differed  widely  from  Hradley's  view  that  the  subject  in 
every  judgment  is  reality  or  sonu'  definite  and  therefore  con- 
crete portion  of  reality.  The  ipsa  res  of  Kant's  formula  is  just 
this   presented   reality   to   which   the   ideal   contcmt   is   referred. 


~  Introduction   to  Loi/ic,  oil.  D,  ji.  ;iti7. 


142  FOOTNOTES  TO  FORMAL  LOGIC 

However  much  we  may  differ  from  Bi-adley's  theory  of  judg- 
ment, it  seems  to  me  that  his  central  contention  that  the  subject 
is  a  concrete  datum  is  unescapable.  I  do  not  see  therefore  that 
Kant's  supreme  rule  differs  essentially  from  Bradley's  definition 
of  inference  as  the  indirect  reference  of  a  content  to  reality. 
The  ideal  content,  meaning,  or  attribute  is  attached  to  reality, 
not  directly  but  indirectly  by  being  joined  to  a  meaning  already 
attached. 

The  second  objection  to  the  formula  is  tliat  it  makes  one  attri- 
bute qualify  another.  This,  too,  seems  an  immaterial  criticism. 
In  the  first  place  we  may  contend  that  there  is  nothing  contra- 
dictory in  the  statement  that  there  may  be  an  attribute  of  an 
attribute,  as  Joseph  seems  to  imply.  Wherever  an  object  admits 
rank  or  psychological  priority  among  its  attributes,  a  later  attri- 
bute, being  an  attribute  of  an  object  already  qualified,  is  in 
reality  an  attribute  of  an  attribute.  Also  the  varying  degrees 
in  intensity  of  the  quale  of  sensations  are  in  a  sense  qualities 
of  qualities.  But  admitting  that  there  may  be  an  inherent  diffi- 
culty wath  the  conception  of  an  attribute  of  an  attribute  (con- 
struing the  expression  literally)  I  thmk  this  is  not  precisely  the 
meaning  tliat  Kant  intended  by  the  expression  nota  notae.  Mark 
of  a  mark,  is  the  better  rendering  of  noia  notae  than  attribute 
of  an  attribute.^  The  working  of  Kant's  formula  may  be  illus- 
trated in  the  syllogism,  Savages  are  cunning,  Indians  are  savages, 
therefore  Indians  are  cunning.  Cunning  is  the  mark  of  savagery, 
and  savagery  is  the  mark  of  the  Indian,  therefore  cunning  is 
the  mark  of  the  Indian.  Of  the  three  terms  in  the  syllogism  two 
are  always  taken  in  connotation,  namely,  the  major  and  the 
middle.  The  minor  must  always  be  taken  in  denotation.  In  the 
major  premise,  both  subject  and  predicate  are  taken  in  connota- 


8  Tt  must  be  observed  that  the  word  7narl-  has  two  iiieauiugs.  It  points 
both  forward  and  backward ;  it  is  the  sign  or  evidence  of  something  that 
has  been,  as  well  as  the  prophecy  of  something  yet  to  come.  The  glacial 
scorings  are  the  marks  of  the  ice-age,  while  a  red  sunset  is  the  mark  of  an 
impending  storm. 


TIN':  CASE  AdAISST  THE  SYLI.OdlSM  143 

lion;  it  affirms  that  tin*  alt  i-ihiitc  of  cinniiiig  accompanies  the 
atti'il)ut(!  of  savagery.  J>ii1  in  tli<'  'iiiiioi-  j)i't'niisc  only  the  i)i'('(li- 
cate  is  taken  in  connotation. 

Kant  maintained  that  the  did n in  <lc  (niuii  was  subordinate 
to  his  formula,  "Whatever  is  a  mark  oi  a  mark  of  a  thing  is  a 
mark  of  the  tlnng  itself."  The  former  declares  that  whatever  is 
true  of  the  concept  is  true  of  everything  contained  under  it. 
This,  accoi'ding  to  Kant  represents  a  stage  in  the  pi'ocess  of 
abstraction  one  ste])  removed  from  llie  formula.  The  concept 
itself  was  derived  in  the  first  instance  by  abstraction  from  the 
things  which  came  under  it.  Thus  whatever  belongs  to  this 
concept  will  in  truth  be  an  attribute  of  an  attribute  and  therefore 
an  attribute  of  the  things  from  whieli  it  has  been  abstracted. 

Kant  drew  a  distinction  between  pure  and  hybrid  mediate 
inferences,  that  we  have  lost  sight  of  in  our  later  discussions 
about  the  universality  of  the  syllogism.  The  pure  inferences 
are  those  which  require  but  three  propositions.  We  have  a  hybrid 
inference  when  between  two  of  the  main  propositions  there 
must  be  interposed  a  fourth  proposition  which  is  itself  an  imme- 
diate inference  from  one  of  the  others.  Kant  made  this  distinc- 
tion the  starting  point  of  his  essay  on  ' '  The  Mistaken  Subtlety  of 
the  Four  Figures."  He  regarded  the  first  figure  only  as  pure 
rationcination,  since  it  involved  never  more  than  three  propo- 
sitions. 

It  is  not  my  purpose  to  enter  into  a  long  discussion  of  the 
relation  of  the  later  figures  to  the  first.  Without  detailed  proof 
I  shall  say  tliat  I  believe  Kant's  position  to  be  fundamentally 
correct.  I  am  sure,  also,  that  Kant  would  have  explained  all  of 
the  modern  asyllogistic  types  of  reasoning  as  "hybrid  inferences." 
In  his  exposition  of  the  fundamentals  of  Symbolic  Logic,  Russell 
has  postulated  ten  indemonstrable  axioms,  the  sixth  of  which  is 
the  syllogism  as  it  is  commonly  understood.  But  on  our  wider 
interpretation  of  the  syllogism,  I  believe,  all  of  the  other  axioms 
can  be  explained     as  either  abbreviated  or  expanded  forms  of 


144  FOOTNOTES  TO  FOEMAL  LOGIC 

the  fundamental  syllogistic  fact — thought  exhibiting  itself  in 
the  triadic  relationship  of  universal  particular  and  singular. 
Let  me  explain  by  quoting  RusselPs  seventh  axiom:  "If  q 
implies  q  and  r  implies  r,  and  if  p  implies  that  q  implies  r,  then 
pq  implies  r.  This  is  the  principle  of  import atimi.  In  the  hypo- 
thesis we  have  a  product  of  three  propositions ;  but  this  can  of 
course  be  defined  by  means  of  the  product  of  two.  The  principle 
states  that  if  p  implies  that  q  implies  /■,  then  ;•  follows  from  the 
joint  assertion  of  p  and  q.  For  example:  'If  I  call  on  so-and-so, 
then  if  she  is  at  home,  I  shall  be  admitted.'  '"■^  I  fail  to  see  why 
this  can  not  be  explained  as  a  triadic  relation.  In  fact,  Russell 
seems  to  resort  to  such  an  explanation  himself  when  he  says 
that  the  hypothesis,  although  it  has  ihrce  propositions,  can  be 
defined  by  two.  Every  thought  contains  three  and  only  three 
terms,  that  is,  there  are  only  three  fundamental  nodes  or  beats. 
This  needs  further  elucidation.  All  reasoning  is  (as  Ave  have 
often  had  occasion  to  remark)  a  movement  from  particular  to 
particular  via  the  universal.  It  follows  that  every  inference 
must  have  three  terms,  and  that  no  inference  can  have  less  nor 
more.  Inferences  have  often  to  do  with  more  than  three  facts. 
But  it  is  important  to  distinguish  between  terms  of  inference, 
that  is  the  significant  nodes  in  the  movement  of  thought  and  the 
data  of  inference,  that  is,  any  accidental  halting-places.  Each 
of  the  three  terms  may  be  viewed  as  a  system  and  when  its 
secondary  data  are  combined  with  the  secondary  data  of  each  of 
the  others,  we  get  hybrid  inferences  with  apparently  more  than 
three  terms.  To  use  a  railway  figure  of  speech,  the  main  trunk 
line  of  thought  has  three  stations  where  the  "train  of  thought" 
must  stop.  There  may,  be  any  number  of  intermediate  stations, 
however,  where  it  may  stop. 

There  have  been  many  attempts  to  give  a  syllogistic  demon- 
stration of  the  so-called  axiomatic  truths  and  many  refutations 
of  these  attempts.     Bradley  has  said,     "To  prove  .syllogistically 


^J  Principles  of  Mathematics,  p.   16. 


THE  CASK  ACAISST  Till'.  SVLLOCISM  145 

that,  Ix'causc  .1  and  ('  aic  liotli  r(jiial  to  />'.  tlu-y  are  equal  to  one 
another,  is  (|iiilc  imiiossihlc "  Also,  "I  may  suggest  to  the 
inatheniatical  ioj^iciaii  timt,  so  long  as  lie  fails  to  treat  (for 
example)  sueli  simple  arguments  as  ''A  before  li,  and  li  with  (', 
therefore  A  before  (',"  he  has  no  striet  right  to  denuind  a  hcai'- 
ing."'"  Euelid's  first  axiom,  "Things  t'qual  to  tiic  sanir  thing 
are  equal  to  each  oilier."  has  been  written  in  syllogistic  form 
thus: 

Tliiiiirs  ('(iiial  to  tlic  siiiiic  tliiiij^  ai-c  e(|u;il  to  I'acli  otlier. 
A  and  ('  arc  things  (Miual  to  tlic  same  thiiiy. 
And  .-.  ./  ('  :\io  (Mjual  to  cacli  otlicr. 

But  in  this  syllogism  both  tlie  major  and  the  minor  premises 
are  defective.  The  major  premise  in  the  syllogism  is  the  axiom 
itself,  and  hence  not  a  major  premise  in  the  required  sense  of  the 
word.  It  would  be  cii'cular  reasoning,  vicious  in  the  first  degree 
to  use  the  identical  proposition,  which  is  to  be  proved.  The 
major  premise  ought  jirojierly  to  read.  Tilings  equal  to  11  tin 
equal  to  each  oilur.  \\\\\  a  more  serious  fault  we  find  in  the 
minor  term,  A  and  (\  In  tiie  concrete  instance  of  the  axiom 
A  =  B,  B  ^  C  .-.  A=^  C.  A  and  C  function  separately  each  as 
a  distinct  subject.  But  in  the  minor  premise  of  the  syllogism, 
by  means  of  which  we  attempt  to  validate  the  axiom,  we  take 
unwarranted  liberties  with  A  and  C  by  attempting  to  make 
them  function  conjointly  as  a  single  subject.  A  and  B  are,  is  not 
the  same  as  A  is  and  B  is.  It  is  not  the  intention  of  the  axiom  to 
assert  a  i)re(lieate  of  A  and  B  as  one.  but  to  deelai'c  a  ri'lation 
between  tl!<'iii.  The  distinction  lietwceii  tlie  collective  and  the 
distributive  use  of  the  t(>rms  is  here  in  question  and  it  is  a  form 
of  the  familiar  fallacy  of  (•omj)osition  of  eli'mentary  logic  that  is 
committed. 

The  argunu'ut  a  fortiori.  ""A  is  greater  than  B,"  **/?  is  greater 
than  f'/' therefore, ''.1  is  greater  than  r."has  been  offered  as  an 


10  Principles  of  Logic,  pp.  H-i9,  360. 


l-iG  FOOTNOTES  TO  FOEMAL  LOGIC 

illustration  of  a  syllogistic  reasoning.  This,  however,  may  be 
expressed  in  the  following  valid  syllogism.  Major  premise.  All 
cases  where,  of  three  things,  the  first  is  greater  than  the  second 
and  the  second  greater  than  the  third,  are  cases  where  the  first 
is  greater  than  the  third.  Minor  premise.  A,  B,  C,  is  a  case 
where,  of  three  things,  the  first  is  greater  than  the  second  and 
the  second  greater  than  the  third.  Conclusion.  A,  B,  C,  is  a  case 
where  the  first  is  greater  than  the  third. 

Here  again  a  criticism  has  been  raised  similar  to  that  which 
we  have  just  examined  in  the  case  of  the  axiom  of  equals.  It  is 
true  that  these  so-called  asyllogistic  forms  of  reasoning  are  not, 
when  reduced  to  the  syllogism,  strictly  formal.  But  neither  are 
they  strictly  material.  From  the  two  propositions  ^'A  is  the  son 
of  C,"  and  "C  is  the  son  of  D,"  we  may  infer  that  "D  is  the 
grandfather  of  A."  This  is  semiformal.  It  is  a  valid  infer- 
ence only  to  one  who  also  knows  the  "system  of  relationships." 
But  granted  this  prior  knowledge,  the  inference  within  this 
"system"  is  evidently  formal  and  capable  of  reduction  to  the 
syllogism.     The  same  is  true  of  the  other  a  fortiori  arguments. 


CHAPTER  VIII 
NOVELTY  AND  I  DENT  [TV  TX  TXFEREXCE 

I 

I  find  (l('i)loi'al)le  disorder  and  obscurity  in  current  discus- 
sion concerning  novelty  and  sameness,  difference  and  idi-niiiy, 
objectivity  and  subjectivity,  independence  and  dependence  in 
judgment.  Some  of  these  difficulties  we  met  in  the  previous 
essay.  I  wish  now  to  call  attention  to  some  further  related 
problems. 

The  New  Logic  asserts  that  the  uni(iueness  of  any  mental 
fact  is  always  of  vital  importance  for  some  specific  purpose ; 
that  in  truth,  its  uniqueness  or  individuality  is  driven  in  upon  it 
from  out  of  that  external  purpose.  We  have,  here,  a  new  and 
revolutionaiy  defiiiiliou  of  essence.  The  essence  of  the  fact 
de])ends  for  its  essential  essence  (if  one  may  be  permitted  such 
ix'duplieation)  upon  the  varying  purpose  to  which  it  may  be 
put.  Li  other  words  there  is  no  essence  in  the  traditional  sense, 
since  the  fact  lias  no  individuality,  no  character  of  its  own. 
This  doct!-ine,  when  applied  witliout  reserve,  leads  inevitably 
to  tlie  conclusion  that  there  is  no  stability  within  the  states  of 
consciousness — that  there  are  no  laws  of  thought.  And  this 
issue  the  pragmatist  accepts  not  reluctantly,  but  even  more  joy- 
fully than  the  ancient  sceptics.  Tn  so  far  as  we  must  take  a  risk 
in  judgment,  each  situation  is  a  law  unto  itself.  The  old  ideal- 
ists uphold  llic  law  that  there  shall  he  law.  The  new  theory 
recognizes  only  one  law,  namely,  the  law  that  there  shall  be  no 
law.  However,  as  we  saw  when  discussing  the  nature  of  judg- 
ment, no  idealistic  theory  of  predication  denies  the  novelty  that 
comes  with  the  i)redic'ate.     Some  risk  we  do  take,  and  must  take. 

I   147  I 


148  FOOTNOTES  TO  FOEMAL  LOGIC 

But  something  over  and  above  risk  there  must  he  in  every  judg- 
ment. That  which  enables  the  risk  to  know  itself  to  be  a  risk  is 
a  stable  principle  of  values. 

There  are  three  possible  views  that  we  may  take  upon  the 
question  of  the  relation  of  stability  to  risk :  Either  there  is  all 
stability  and  no  risk,  as  an  absolute  idealist  might  aver ;  or  there 
is  no  stability  and  all  risk  as  the  pragmatist  in  my  opinion  is 
compelled  to  say ;  or  there  is  some  stability  and  some  risk  as  the 
dynamic  idealist  holds.  If  practical  consequences  are  the  sole 
test  of  truth — if  the  object-matter  of  judgment  is  brute  force — 
then  thinking  is  indeed  pure  adventure.  But  I  submit  that  it  is 
one  thing  to  say  that  judgment  is  practical  and  hence  riskful, 
and  quite  a  different  thing  to  say  that  there  is  nothing  else  to 
judgment  but  its  utility  and  risk.^  As  Professor  Hocking  has 
said  with  such  picturesque  vigor:  "Only  he  who  has  tried  (or 
tried  to  imagine)  a  pure  adventure  knows  that  there  is  no  sudi 
thing  as  a  pure  adventnre;  for  when  you  have  cancelled  path, 
peak,  sky,  star,  all  distinguishable  points  in  space,  the  adventure 
itself  is  abolished."^" 

We  have  sufficiently  insisted  that  no  relation  can  dispense 
with  either  of  the  two  aspects  the  within  or  the  hctiveen.  A 
relation  that  attempts  to  exhibit  identity  without  difference,  or 
difference  without  identity  is  no  genuine  relation,  since  it  omits 
one  or  the  other  of  these  two  aspects.  For  this  reason,  as  Bosan- 
quet  has  pointed  out,  no  single  judgment  can  exhibit  a  com- 
plete comparison ;  a  disjunctive  judgment  either  implied  or 
expressed  is  required.  Every  act  of  relating  is  an  act  of  com- 
parison, and  comparison  always  affirms  the  interdependence  of 
identity  and  difference — it  is  redintegration.     When  we  assert 


1  Cf.  Bradley,  Principles  of  Logic,  pp.  18,  499.  ' '  The  assertion  we  are 
to  examine  is  not  that  practical  influence  induces  us  to  judge,  or  results 
from  a  judgment:  What  is  asserted  is  that  judgment  is  nothing  else 
whatever.  .  .  .  We  do  not  mean  to  ask  what  sound  performances  of 
reasoning  are  practical)le,  but  what  types  of  argument  are  flawless  in 
themselves,  without  regard  to  the  question  if  any  one,  or  no  one,  can  use 
them  in  his  work. ' ' 

1"  Meaning  of  God  in  Human  Experience,  p.  xii. 


NOVELTY  AND  IDENTITY  IN  IXEEHEXCE  149 

that  every  judgment  affirms  or  (Icnics  an  identity  in  iIk;  midst  of 
difference,  and  difference  in  the  midst  of  identity,  this  must  be 
taken  to  moan  that  we  cannot  begin  with  one  ■dloint  and  super- 
impose the  other  upon  it  as  an  after-effect,  lioth  are  present  in 
one  indivisible  moiiicnt  of  consciousness.  Although  the  differ- 
ence and  the  itU^ntity  are  concomitants  in  every  judgment,  the 
dominant  emphasis  may  be  shifted  from  one  component  to  the 
other.  Both  may  be  quite  indistinct  in  the  first  suggestion  and 
the  judgment  may  l)e  aimed  [Ji'imarily  to  develop  this  inchoate 
distinction.  Again  one  aspect  in  the  presented  eorrelation  may 
be  faint  and  the  other  vivid ;  here  the  judgment  will  aim  to 
reestablish  the  balance  by  emphasizing  the  weaker  aspect.- 

In  his  criticism  of  the  three  fundamental  laws  of  thought  of 
Traditional  Logic,  Hegel  proved  that  the  Law  of  Identity  liter- 
ally interi)reted,  cannot  i)Ossibly  be  an  expression  of  the  activity 
in  any  phase  of  a  living  judgment.  If  A  is  A.  states  a  sheer 
tautology,  it  is  no  judgment.  It  proposes  to  say  something,  but 
ends  by  saying  nothing.  It  is  worse  than  idle  breath,  for  it  has 
not  even  asserted  identity.  The  real  Law  of  Identity  "A  is  A" 
means  that,  whatever  is  true  of  A  in  one  reference  is  true  in 
another.-' 

The  difficulty  about  the  conception  of  identity  and  difference 
would  l)e  less  puzzling  if  instead  of  the  conjunction  and,  we 
used  sonu>  other  word  to  describe  the  I'elation  involved,  for 
example,  identity  in  or  with,  or  hccansc  of  dittV'rence.  And  is  a 
highly  ambiguous  word.  In  Symbolic  Logic  it  has  been  found 
very  necessary  to  distinguish  among  its  several  meanings.  For 
the  present  discussion  the  obvious  warning  is  that  and  must  not 


-  Bosanquet,  Logic,  I,  30.  "As  regards  the  aflSnity  between  Distinc- 
tion and  Identification,  they  are  obviously  two  sides  of  the  same  process 
and  it  is  idle  to  ask  which  came  first.  So  far  as  we  can  see,  Consciousness, 
or  at  least  Intelligence,  must  begin  with  both." 

s  Synd)olic  Logic  which  is  rendering  a  most  important  service  to  exact 
thinking  offers  a  definition  of  identity  that  is  quite  free  from  the  per- 
plexing ambiguities  that  have  beclouded  it  in  the  past.  Cf.  Russell, 
Frincipli's  of  Mathematics,  p.  20.  "  X  is  identical  with  Y  if  Y  belongs  to 
every  class  to  whi(di   X  belongs." 


150  FOOTNOTES  TO  FOBMAL  LOGIC 

be  taken  to  indicate  mere  juxtaposition.  If  that  were  all  the 
and  signified,  then  the  whole,  within  wliich  the  identity  and 
difference  are  aspects,  would  be  no  genuine  whole :  for  either 
aspect  might  be  removed  and  the  other  would  suffer  no  change 
in  meaning.  The  limiting  conceptions  for  identity  in  difference 
are  at  the  lower  limit,  pure  tautology,  at  the  upper  limit,  entire 
difference.  But  obviously  these  limits  can  never  actually  be 
reached  by  the  judgment  without  sacrificing  its  essential  char- 
acter. The  judgment  indeed,  aims  both  at  mere  tautology,  and 
mere  difference,  but  if  it  found  its  goal  it  would  lose  its  life — 
the  reverse  of  the  scriptural  experience  of  losing  life  to  find  it. 

In  this  modern  indictment  of  the  old  Logic  a  most  serious 
arraignment  on  all  sides  is  made  against  the  traditional  laws  of 
thought.  But  every  argument  against  any  one  of  these  three 
laws  always  presupposes  one  or  all  of  them.  Every  argument 
against  identity  assumes  a  principle  of  identity.  The  opponent 
of  the  Law  of  Identity  must  be  standing  upon  a  platform  sup- 
ported by  stable  values  when  he  assaults  identity,  otherwise  his 
aim  will  be  uncertain  and  he  will  miss  the  mark  as  widely  as  a 
Jiowitzer  anchored  upon  a  drifting  cloud.  These  attacks  upon 
the  law  of  identity  are  most  surprising  instances  of  oversight. 
Reason  cannot  commit  suicide.  A  law  of  thought  is  reinstated  in 
each  attempt  to  remove  it.  The  Aristotlian  logic  is  the  founda- 
tion of  all  logic  even  of  those  which  attempt  to  overthrow  it.^ 

No  judgment  affirms  mere  identity.  If  any  collection  of 
words  should  aim  to  assert  identity  they  would  not  constitute  a 
judgment,  for  as  Hegel  said,  they  would  sin  against  the  essential 


4  Sidgwick,  Eleinottar)/  Logic:  "It  is  indisputable,  e.g.,  that  every 
A  is  A,  but  this  leaves  it  quite  uncertain  whether  any  actual  case  of  'A' 
that  yve  meet  with  is  the  genuine  thing  or  not.  Such  a  'law'  therefore 
has  no  application  except  on  the  assumption  that  we  no  longer  need  the 
information  that  it  is  supposed  to  give.  This  kind  of  indisputability  is 
common  enough,  and  we  can  all  manufacture  as  much  of  it  as  may 
content  us."  (p.  120.)  "A  is  prima  facie  A,  and  not  non-A,  and  clearly 
distinct  from  B.  But  if  A  can  be  A  for  one  purpose  and  non-A  for  another 
the  supposed  authority  of  these  rules  //(  application  crumbles  away  to 
nothing."    (p.  157.  j 


NOVELTY  AM)  IDF-STirV  IS  I S l-KUENCE  151 

fharaetcrislic  ui'  judt^uicnl.  lUit,  on  llie  other  luunl,  witliout  the 
tacit  assumption  of  identity,  no  affirmation  or  denial  could  ever 
be  made.  Sameness  and  dilTcivnce  are  so  inter-related  that  they 
are  in  reality  diff<'rcnt  sith-s  of  the  self-same  content.  Any  two 
facts  that  fail  within  the  same  whole  are  alikf  and  yet  different. 
Nevertheless,  although  likeness  is  a  fact  and  difference  is  a  fact, 
we  never  mean  to  assert  just  the  fact  of  likeness  or  the  fact  of 
difference.  This  is  the  puzzle  which  Professor  Dewey  has  made 
the  basis  of  his  criticism  of  all  conceptual  logic.  He  says,  in 
criticism  of  all  such  logics,  "The  rock  against  wliicli  every  such 
logic  splits  is  either  that  reality  already  has  the  statement  which 
thought  is  endeavoring  to  give  it  or  else  it  has  not.  In  the  former 
case  thought  is  futilely  reiterative ;  in  the  latter  it  is  falsifica- 
tory.''  I  shall  attempt  to  show  in  detail,  later  that  these  two 
alternatives  do  not  exhaust  the  i)Ossible  i)oints  of  view.  We  may 
answer  both  charges  of  futility  and  falsity  by  saying  that  the 
predicate  is  something  which  the  subject  already  is  or  Jia.s^  but 
which  it  was  not  known  to  be  or  to  have  prior  to  the  predication. 
In  his  defense  of  independence  the  realist  assumes  a  mind 
which  is  to  know  a  totally  independent  and  hitherto  unknown 
object.  He  then  graduall\'  l)i'ings  that  object,  so  to  say,  toward 
the  mind  until  the  mind  observing  it,  seizes  it,  and  knows  it.  He 
admits  that  in  any  such  act  of  normal  thinking,  when  the  object 
is  known,  that  knowing  of  it  causes  it  to  enter  into  a  new  relation. 
l>ut  lie  eiiipliatically  declares  that  certain  other  I'elations  the 
object  retains,  and  that  these  are  in  no  wise  influenced  by  the 
new  relation  of  the  knowledge  it  has  permitted  to  be  set  up.  But 
now  is  it  not  an  unwarranted  abstraction  by  means  of  which  the 
realist  transcends  the  unity  of  knowing  and  being,  and  imagines, 
or  conceives,  or  tiiinks  an  object  independent  of  all  knowing? 
When  we  separate  being  from  knowing,  reality  from  thought, 
what  is  left  is  not  just  an  independent  unknowable  something, 
but  real  non-being.  Whoever  declares  that  the  objects  of  sense 
perception — -or  the  objects  of  thought — are  not  in  tliemselves  as 


152  FOOTNOTES  TO  FOEMAL  LOGIC 

they  appear  to  us  is  making  an  assertion  for  which-  there  is  no 
logical  defense  whatever.  In  order  to  pronounce  the  things  in 
themselves  other  than,  or  independent  of,  the  appearaneeSj  we 
must  previously  have  compared  the  things  as  they  are  with  the 
things  as  they  appear.  If  this  can  be  done  then  the  independ- 
ence has  been  disproved  before  we  begin,  and  we  are  guilty  of  a 
negative  petitio. 

The  realist  in  every  age  has  put  the  burden  of  proof  or  dis- 
proof, upon  the  idealist.'^  He  says  that  entities  are  independent, 
unless  they  are  proved  dependent.  This  is  analogous  to  the 
familiar  legal  procedure  of  regarding  a  man  innocent  until  he  is 
proved  guilty.  That  there  is  an  important  element  of  truth  in 
this  principle  in  legal  practice  I  am  not  concerned  to  deny.  In 
the  law  with  which  we  are  dealing,  approximations  to  certainty 
merely,  and  the  principle  of  the  presumption  of  innocence  is  all 
we  have.  But  in  logical  problems  where  rigorous  demonstration 
is  sought,  it  is  a  confession  of  weakness  to  give  external  evidence 
where  internal  proof  should  be  forthcoming. 

The  realist's  definition  of  independence  as  equivalent  to  non- 
dependence  is  open  to  serious  objections.  In  this  definition  he 
has  failed  to  distinguish  between  the  absence  of  dependence  and 
the  opposite  of  dependence.  The  realist  admits  that  he  cannot 
prove  independence  until  the  idealist  has  failed  to  prove  depend- 
ence. Let  us  accept  his  challenge  and  attempt  to  prove  that 
there  is  ineffaceable  dependence  between  idea  and  object.  The 
realist  asks  us  to  go  to  experience  for  the  confirmation  of  his 
doctrine.  Objects  in  the  world  of  matter  he  says  are  independent 
of  one  another ;  so  too  are  ideas  in  the  world  of  mind.  Up  in 
Lake  Superior,  and  quite  on  the  bottom,  he  tells  us,  is  a  drop  of 
water,  and  here  are  pages  in  a  book.  They  are  totally  inde- 
pendent, are  they  not  ?  The  turning  of  the  pages  in  no  wise 
disturbs  the  essential  being  of  that  drop  of  water.    And  there  is 


5  E.g.,  E.  B.  Perry,  "  Eealistic  theory  of  iudependenee, "  Neic  Eealisrn 
(New  York,  Macmillan,  1912),  p.  99. 


NOIKI/IV  AM)   IDESTITV  J\   INFERENCE  15:{ 

llalU-y  '"^  Comet,  wiuj^iiij^  its  way  througli  space  preijaratory  to 
coining  back  to  us  again  in  seventy  years.  That,  too,  the  realist 
says  is  iiidcpciKlciil  ol'  this  page.  But  now  when  we  enter  the 
reahu  of  possibilities,  ai'c  tlirse  facts  of  oui'  illustration  so  inde- 
pendt'Ut  as  they  seem  at  first  sight?  The  drop  of  water  at  the 
bottom  of  Lake  Superior  may  conu'  to  the  surface,  evaporate, 
enter  the  atmosphere,  be  carried  to  this  spot  and  fall  upon  this 
page  and  blur  the  ink — tiiat  is  a  possibility.  Therefore,  in 
ei'iticism  of  New  Realism  the  idealist  insists  that  this  possibility 
which  is  at  tlic  heart  of  the  diop  of  wat(M'  is  alread\'  a  pai't  of 
its  Ix'ing,  as  it  lies  tiiei-e  at  the  bottom  of  the  lake  Tin-  vri-y 
possibility  of  its  entering  into  harmful  relations  with  my  j^aper, 
prevents  it  from  being  regarded  as  an  absolutely  independent 
existence.  It  is  an  uncombatted  possibilit,\'  ami  therefoi-e  an 
actuality.  Hence  the  idealist  refuses  to  admit  that  even  in  our 
concrete  human  experience,  we  can  ever  find  two  jihysical  objects 
which  are  so  utterly  indej)endcnt  of  each  other  that  no  conceivable 
change  in  one  of  them  can  effe(;t  the  other  in  any  wise. 

But  we  need  not  rely  alone  upon  tliis  argument  from  the 
possihilitics  that  lie  inherent  in  the  dro])  of  water.  That  drop 
of  water  has,  at  this  vciy  moment,  a  relation  to  this  paper — a 
relation  that  differs  only  in  degree  and  not  in  kind  from  the 
relation  which  it  would  have  to  the  paper  if  it  were  actually 
lying  here  now  and  blurring  the  words  as  they  are  being  read. 
The  I'calist  would  hardly  venture  to  claim  that  space  is  more 
than  a  principle  of  differentiation.  As  I  have  already  said,  the 
realist  declares  that  whenevei-  we  know  any  object  (not  our- 
selves) this  object  is  existent ially  absolutely  independent  of  our 
knowledu-,.  of  the  object.  So  that  [he  ideas  that  constitute  our 
knowledge  nuiy  come  antl  go,  they  nuiy  be  true  or  false,  and 
yet  the  object  will  renuiin  forever  what  it  was.  In  knowing  the 
rest  of  the  universe  other  than  ourselves,  we  know  something 
that  is  different  fiom  that  knowledge,  and  because  different  is 
indei)endent  of  that  knowledge.  And  here  is  the  novelty,  the 
risk,  the  objectivity  in  judgment  that  can  never  be  effaced. 


154  FOOTNOTES  TO  FOllMAL  LOGIC 

For  further  i)roof  of  this  metaphysical  doctrine  of  inch^pend- 
ence,  the  new  realist  refers  us  to  the  mathematical  theory  of  prob- 
abilities, Avhere  events  are  said  to  be  mutually  independent.  In 
the  throwing  of  dice,  for  example,  each  throw  is  independent  of 
the  others.  But  again  we  should  insist  that  when  we  look  closely 
at  all  such  illustrations  of  independence,  we  find  that,  in  the  last 
analysis,  the  objects  so  defined  are  always  relative.  This  is 
pseudo-independence ;  we  are  looking  merely  at  special  aspects 
of  our  objects.  To  use  a  crude  but  pertinent  illustration — our 
fingers  ma}'  be  said  to  be  separate  and  independent  when  we  view 
them  at  their  tij^s,  and  do  not  follow  them  back  to  their  physio- 
logical connection  at  the  palm.  The  two  throws  of  the  dice  which 
the  realist  uses  to  support  him  in  his  metaphysical  gamble  in 
the  search  for  independence,  are  connected  in  the  general  causal 
arrangement  of  our  universe ;  they  are  really  not  wholly  inde- 
pendent. We  merely  do  not  happen  to  know  what  the  causal 
connection  is.  When  we  speak  of  pure  chance  we  overlook  these 
causal  features  and  fail  to  observe  that  any  two  physical  events 
occur  in  the  same  space,  and  in  the  same  time.  The  parts  of 
space  and  the  moments  of  time,  are  perceptually,  genuinely  inter- 
dependent. Space  and  time  are  not  principles  of  individuation, 
and  nothing  short  of  the  individual  can  be  regarded  as  genuinely 
independent.  However  far  apart  two  objects  are  placed,  they  are 
still  clutched  in  the  enwholing  grasp  of  space  and  cannot  be 
totally  indifferent  to  each  other.  Space  is  a  principle  by  means 
of  which  things  are  "coupled  apart."  In  the  theory  of  probabili- 
ties, we  do,  to  be  sure,  call  two  events  that  happen  in'  the  same 
space  and  in  the  same  time  independent  events.  What  we  mean 
is,  not  that  these  two  events  are  absolutely  independent,  but  that 
there  is  an  aspect  in  which  we  may  treat  them  as  independent. 
For  certain  purposes,  we  may  ignore  their  interdependence  or 
at  any  rate  treat  it  as  insignificant,  and  thus  secure  an  apparent 
independence. 

It  is  precisely  this  i:)seudo-independence  which  the  new  realist 


NOrHLTY  A.\n  inKSTITV  IS  ISI' l-.ni'.SCE  155 

has  seized  upon  and  nia^-nificd  into  a  ^enuiiif  inde|)end('nci'.  The 
realist's  explanation  of  the  process  of  knowing,  as  Bradley  would 
say,  is  a  "makeshift,  a  device,  a  mere  practical  compromise," 
which  cannot  l)e  lojj:icall>'  defended.  From  otie  point  of  view  we 
have  to  take  i-eality  as  iiiany,  and  fi-oni  another,  as  one — an 
ontological  dualism  and  an  epistemological  monism.  We  insist 
on  dividing  reality  for  the  purposes  of  existence,  or  to  take  it,  if 
we  wish,  as  indivisible  for  the  purpose  of  knowledge. 

Tile  idealist  says  that  the  alleged  objects  independent  of 
consciousness  are  objective  and  independent  only  in  the  sense 

that  they  are  the  externalization  of  an  internal  constraint.    They 

are  what  wev^usfc,  think,  if  thought  is  to  be  self -consistent.  Our 
apparent  success  is  won  by  a  perpetual  sliit'ting  of  the  ground, 
so  as  to  turn  our  backs  upon  the  aspect  we  desire  to  ignoi-e.  But 
when  these  inconsistencies  are  brought  together,  as  in  rigid  Logic 
they  must  be,  the  result  is  an  incurable  discrepancy.  The  inde- 
pendent beings  of  which  the  realist  speaks  are  beings  that  have 
no  common  features,  no  ties,  no  relations,  or  at  any  rate  onl}'  that  \  . 
mysterious  kind  of  relation  which  he  calls  mere  dependence.  They 
are  separated  one  from  tlic  other  by  an  alisolutely  impassable 
chasm.  But  such  beings,  we  insistently  repeat,  cannot  be  in  the 
same  space  or  the  same  time,  or  be  membei's  of  the  same  con- 
ceptual realm.  They  are  false  existences,  and  vanish  at  the  touch 
of  tliought  into  the  realm  of  non-being.  They  are  not  one.  nor 
many,  but  just  impossible  nothings — just  the  drapery  folded 
around  the  empty  outline  of  ghosts  of  beings. 

The  realist  insists  that  real  beings  must  be  essentially  and 
absolutely  indei)endent.  In  order  to  get  sueh  independent  beings, 
lie  first  declares  that  certain  gaps  or  barriers  are  absolute.  But 
he  forthwith  proceeds  to  make  thought  ti-anscend  these  very 
barriers.  He  accomplishes  this  feat  by  an  actual  union  of  those 
])arts  of  being,  which  in  the  first  instance  he  attempted  to  put 
forever  asunder.  Realism  attempts  to  divide  the  what  of  an 
object  from  its   tJiat — tiie   meaning  from   its  existence — a  vivi- 


.V 


156  FOOTNOTES  TO  FOEMAL  LOGIC 

section  that  must  always  prove  fatal.  It  is  true  that  a  ijsycho- 
logical  dualism  is  implied  in  the  very  conception  of  conscious- 
ness. But  as  we  have  seen  earlier  this  postulated  objectivity  does 
not  imply  the  ontological  pluralism  which  the  New  Realism  seems 
to  demand. 

In  the  new  realist's  philosophy,  quite  closely  related  to  the 
doctrine  of  independence  and  the  problem  of  error,  there  is  a 
third  problem  which  is  also  one  of  the  crucial  test  problems  of 
the  realistic  metaphysics — the  ancient  problem  of  the  one  and 
the  many,  the  whole  and  the  part.  One  phase  of  this  problem 
I  have  already  discussed  in  considering  the  doctrine  of  inde- 
pendence. The  realist's  explanation  of  the  relation  between  the 
one  and  the  many  seems  to  me  to  be  a  complicated  linkage  of 
circular  reasoning,  in  which  the  inquirer  is  continually  deluded 
by  an  apparent  approach  to  valid  conclusions,  and  is  yet  all  the 
while  led  back  to  the  point  from  which  he  set  out.  The  realist 
fails  to  reach  any  satisfactory  solution  of  the  problem  of  the 
one  and  the  many,  I  venture  to  think,  because  he  is  applying  an 
inadequate  and  imperfect  conception  of  the  relation  of  whole  to 
part,  and  of  the  function  of  analysis  and  synthesis  in  judgment. 
In  the  world  in  which  the  pragmatist  and  the  new  realist  first 
find  themselves  and  beyond  which  they  hold  they  can  not  go — 
the  empirical,  quantitative  world — the  parts  of  every  whole,  the 
elements  of  every  multiplicity,  stand  in  purely  external  relations 
to  each  other.  This  is  one  of  the  vital  axioms  of  every  form  of 
realism.  Every  other  principle  or  category  that  it  employs,  must 
conform  to,  or  be  a  genuine  expression  of  the  fundamental  char- 
acteristic of  this  phenomenal  world,  the  mutual  exclusiveness,  the 
utter  isolation  of  its  elements. 

But  in  the  world  of  thought,  in  the  qualitative  order,  a  funda- 
mentally difi:'erent  axiom  is  discovered.  Consciousness  is  not  a 
mere  collection  or  aggregate  of  states,  existing  seriatim,  each 
self-sufficient ;  but  it  is  an  organic  whole,  a  genuine  system,  every 
part  of  which  has  meaning  only  in  so  far  as  it  is  related  to  the 


NOrKLTY  AM)  IDKSTITY  IS  INFERENCE  157 

rest.  The  new  realist's  |)i'()l)lfiii  oi"  iiKlciM-iidcuce  presents  no 
difficulty  if  we  accept  Aristotle's  definition  of  a  true  wliolt-,  that 
is,  a  whole  sueli  that  if  any  part  is  modified  or  removed  th<.'  total 
is  entirely  altered;  for  tiiat  of  which  the  presence  or  absence 
makes  no  difference  is  no  ti'ue  part  of  the  whole.  In  the  deep*-!' 
life  of  self-active  mind,  there  is  both  multiplicity  or  diversity ; 
but  it  is  the  multiplicity  or  diversity  that  is  not  of  parts,  opposed 
to  each  other  and  constituting  a  whole  l)y  juxtaposition.  In  the 
organic  whole  of  thought  no  part  has  an  intdligitjle  existence  by 
itself  in  separation  from  the  rest.  Objects  in  tiie  material  order 
are  by  their  very  definition  mutually  exclusive.  Each  object  in 
space  lies  outside  of  every  other,  and  can  be  only  externally 
related  to  them.  But  the  independence  of  the  elements  in  the 
thought  system  is  the  independence  of  that  which  altiiough 
always  limited  is  limited  only  by  what  is  of  the  same  essence  with 
itself.  The  element  in  the  scientific  order  is  an  element  which 
declares  its  independence  of  all  that  lies  without  it.  The  element 
of  thought,  however,  is  an  element  which  is  ever  discovering  itself 
in  that  which  ai)parently  limits,  or  lies  beyond  it. 

II 

All  vocabulary,  and  particularly  English  vocabulary,  is  defec- 
tive in  words  to  designate  tlie  highest  type  of  sijiiHx sis.  that  is, 
the  synthesis  which  does  not  entirely  efface  the  i)arts  in  the 
achievement  of  the  whole.  Also,  we  have  no  good  single  word 
to  embrace  the  two  aspects  of  the  highest  type  of  analysis,  Avhich, 
in  winning  its  part  is  not  totally  disruptive  of  the  whole.  We 
greatly  need  in  this  di.scussion  of  the  essential  import  of  judg- 
ment what  Philosophy  in  every  language  through  all  the  ages 
has  felt  the  lack,  namely  a  single  word  to  denote  aiialysis  in 
synth(sis,  or  synthesis  in  analysis —  the  process  in  which  an 
identity  is  preserved  in  the  midst  of  difference. 

In  the  dialectic  process,  flKsis.  antitJiesis,  and  synthesis, 
namely,  the  positing  of  an  object,  the  placing  over  against  it  its 


l.-)8  FOOTNOTES  TO  FOEMAL  LOGIC 

negative,  and  then  the  reconciling  of  the  two,  vocabulary  follows 
tlionght  with  an  abundance  of  adequate  words  up  to  the  second 
stage.  Language  is  rich  in  words  that  distinguish  the  first  two 
stages,  thesis  and  antithesis;  affirmation  and  denial,  inclusion  and 
exclusion,  and  their  many  synonyms  and  antonyms  cover  satis- 
factorily all  of  the  various  shades  of  meaning  of  the  first  two 
steps  in  thought's  movement  of  increasing  complexity.  But, 
when  we  pass  to  the  third  stage  of  synthesis  and  think  in  terms 
of  a  genuine  reconciliation  of  a  concept  with  its  negative, 
language  refuses  to  follow,  or  at  any  rate  fails  to  provide  a  new 
and  unambiguous  word  to  denote  the  essential  characteristic  of 
the  complex  thought  process  of  this  third  stage — the  stage  of 
higher  synthesis.  The  word  which  seems  most  nearly  to  express 
the  double-acting  character,  the  analytic-synthetic  or  synthetic- 
analytic  process,  in  all  judgments,  or  is  constriction.  As  Bosan- 
quet  says:  "The  process  of  construction  is  always  that  of  ex- 
hibiting a  whole  in  its  parts,  an  identity  in  its  differences ;  that  is 
to  say,  it  is  always  both  analytic  and  synthetic." 

On  the  higher  level  of  synthesis,  when  we  attempt  to  exhibit 
the  results  of  reflective  insight,  we  express  ourselves  imperfectly 
by  circumlocution.  If  we  are  pressed  for  a  single  term  to  describe 
the  third  stage,  we  invariably  employ  the  same  words  to  designate 
the  synthesis,  or  reconciliation  of  the  thesis  with  its  antithesis, 
that  we  have  already  employed  to  designate  the  thesis.  This  has 
given  rise  to  endless  confusion  and  misunderstanding  in  philo- 
sophical discussions.  In  the  time-series,  for  instance,  we  posit 
as  thesis  is,  then  over  against  the  is,  we  place  its  antithesis,  was. 
But  now,  when  we  are  called  upon  to  reconcile  the  two,  when  we 
comply  with  the  inevitable  demand  of  thought  to  discover  what 
thesis  and  antithesis  here  have  in  common,  we  find  not  a  third 
new  word,  but  one  of  the  two  already  employed,  namely,  is.  In 
like  manner,  necessity  and  contingency  are  synthesized  by  neces- 
sity ;  the  one  and  the  many  by  the  one.  We  generally  mark  the 
distinction,    by   capitalizing   the    one   word   in   the    position   of 


NOl'I'.LTV  AM)  inh.SriTV  IS  ISFFJiKSCK  159 

syiitlicsis.  ()!■  \)\  way  ol'  cxi)!;!)!;!!  ion.  we  say  tlial  necessity  is  a 
liiglu'i'  necessity  which  is  the  reconciliation  of  itself  with  tin- 
eontinjjent ;  or  thai  iiiiily  is  a  lii}?]i('r  unity  wiiicli.is  reconciliation 
of  itself  witli  Ihc  many.  The  distinction  between  these  two  niean- 
injjfs  of  is.  \\v  liiid  illiisl  ra1c(l  in  the  sentence.  "  llci'oi-e  Aliraliain 
was,  I  am.'" 

Of  all  onr  English  synoiiytiis  of  analysis  and  synthesis,  the 
words  diffircntiution  and  conslniclion,  best  bring  out  the  revers- 
ible and  transitive  cliaiacter  of  the  process.  Any  i)rocess  of 
genuine  construction  always  exhibits  tlie  final  whole  in  and 
through  its  i)arts.  It  sets  forth  an  identity  in  the  midst  of  its 
difference.  That  is  to  say,  as  Bradley,  Bosanquet  aiul  othei- 
recent  writers  have  pointed  out,  it  is  always  l)otli  analytic  and 
synthetic.  In  any  discussion  of  the  iuteri-elationshi])  between 
analysis  and  synthesis  it  is  ini])ortant  to  distinguish  between 
perceptual  synthesis  of  parts  into  a  whole  in  space  and  time,  and 
conceptual  synthesis  of  parts  and  whole  in  a  non-temporal  order. 
The  result  of  the  former  process  is  always  a  mechanical,  purely 
((uantitative  aggregate.  The  mathenuitieian  has  ever  had  a  clear 
eoncei)tion  of  this  interdependence  of  analysis  and  synthesis.  His 
terms,  integration  and  differentiation,  are  always  employed  in  full 
view^  of  the  vital  correlation  of  parts  and  whole.  It  is  mani- 
festly impossible  in  the  non-metrical  reaches  of  geometry  to  think 
of  this  i-elation  as  one  subsisting  between  ])arts  and  whole  witliout 
confusion,  because  of  the  quantitative  eonnotation  of  the  terms 
part  and  whole  as  we  ortlinarily  employ  them.  The  mathema- 
tician has  tliei'efore  wisely  come  to  prefer  the  terms  element  and 
sjjsd  )n.  Moreover,  in  describing  the  process  of  integration,  he 
is  careful  to  jjoint  out  that  in  the  complex  entirety  into  which 
the  elements  have  been  combined,  the  elements  are  never  impotent 
and  indistinguishable.  And  conversely,  in  the  process  of  dif- 
ferentiation into  elements  the  system  is  iiexci'  dismembered  or 
multilated. 

The  doctrine  tliat  a  jn'oposition  is  analytic  when  the  predicate 


160  FOOTNOTES  TO  FORMAL  LOGIC 

is  a  genus  or  differentia  of  the  subject,  and  synthetic  when  the 
predicate  is  a  proprium,  or  accidens,  is  maintained  by  Welton." 
This  view  obviously  defines  in  a  circle.  It  presupposes  that  we 
can  distinguish  between  the  accidental  and  the  essential  attributes 
of  the  subject,  without  invoking  the  assistance  of  the  very  con- 
ception of  analysis  and  synthesis  which  this  distinction  is  called 
upon  to  define.  If  the  so-called  accidental  attribute  is  accidental 
in  the  literal  sense  of  the  word — if  it  has  drifted  in  upon  the 
subject  like  a  snowflake  out  of  an  unknown  sky — then  it  is  not 
even  a  synthetic  judgment,  it  is  not  a  judgment  at  all.  It  is 
worse  than  sheer  falsehood,  it  is  empty  breath.  However,  if 
instead  of  the  terms  accidental  and  essential  attributes,  we  use 
the  terms  external  and  internal  meanings,  we  may  discover  a 
sense  in  which  we  can  properly  speak  of  analytic  judgment  as 
the  explication,  or  determination  of  internal  meanings,  and 
synthetic  judgment  as  the  implication  or  determination  of 
external  meanings.  But  then,  we  should  be  obliged  to  return  to 
the  view  for  which  we  are  here  contending,  that  analysis  and 
synthesis  are  inseparable,  correlated  aspects  of  every  act  of  judg- 
ment. But  it  should  be  pointed  out  again  that  on  this  view  the 
so-called  accidental  attributes  or  external  meanings  are  not  so 
accidental  and  external  as  at  first  sight  they  appear  to  be. 

The  problem  of  the  true  import  of  judgment  rests  back  finally 
upon  this  distinction  between  external  and  internal  meaning.  If 
we  are  to  rescue  judgment  from  the  fatal  paradox  of  being  either 
false  or  idle,  we  must  show  that  it  is  possible  for  the  subject  to 
have  an  internal  meaning  consistent  with  an  external  meaning 
brought  to  it  by  the  predicate.  Let  us  take  any  diyadic  relation 
in  a  pluralistic  universe.  Let  us  assume,  for  example,  that  A 
and  B  are  two  minds  or  souls  (Kantian  ends),  in  such  a  pluralis- 
tic universe.  A  has  its  internal  meanings,  namely,  a,  h,  c,  d,  etc., 
and  likewise  its  external  meaning  m,  n,  o,  p.  But  on  closer 
analysis  it  is  discovered  that  these  external  relations  m,  n,  o,  p 


6  Manual  of  Logic,  p.  104. 


XorKI.TV  .t.\l)  IDKSTITY  IX  INFERENCE  161 

art*  only  the  (li-iiiaiids  that  hit  iiiadi'  ii]»(jii  A  \)y  li  ami  these 
(Icniaiuls  of  li  arc  />'s  own  internal  nicaiiinf^s,  wiiidi  ai'c  pre- 
cisely the  aforesaid  ni,  )i,  o,  p.  And  in  the  same  way  /is  external 
meanings  will  be  a  demand  made  ui)on  B  by  A  through  its 
internal  meaning  a,  h,  c,  d.  In  short,  yl's  external  meanings  are 
B\  internal  iiieanin^^s:  and  \iee  versa,  /> 's  external  meanings 
are  ^l"s  intei-nal  meanings.  This  logieal  doctrine,  thus  expressed 
symbolically  is  analogous  to  the  definition  of  a  true  j)erson  in 
explanatoi-y  ethics.  There  too,  the  true  insight  is  i-eached  by  a 
reciprocal  determination  of  internal  and  external  meanings.  A 
person  is  being  endowed  with  rights  (internal  meanings)  that  are 
inalienable,  and  duties  (external  meanings)  that  are  absolutely 
binding. 

It  must  be  observed  that  we  deal  with  the  same  reality  whether 
we  approach  it  analytically  or  synthetically.  This  true  insight 
into  the  real  nature  of  analysis  and  synthesis  in  judgment  settles 
finally,  in  my  opinion,  the  much  debated  question  whether  the 
analytic  judgment  is  really  a  judgment,  tbat  is  to  say,  whether 
it  is  not  in  the  last  analysis  idle;  and  the  correlated  question, 
whether  the  synthetic  judgment,  which  is  supposed  to  bring 
novelty  in  the  predicate  is  not  fah( .  The  subject  is  indeed  given 
to  us  by  one  act  of  analytic  attention,  and  the  predicate  by 
another.  But  to  know  the  parts  and  to  know  the  whole  sei^arately 
is  not  the  same  as  to  know  the  j^arts  in  the  whole,  or  the  whole 
containing  the  parts.' 

Now  it  must  be  confessed  that  it  is  difficult  to  tell,  in  the 
analytic  judgment  precisely  where  its  latent  synthetic  aspects 
begin  to  operate,  and.  in  the  synthetic  judgment,  it  is  difficult 
to  tell  at  precisely  what  point  the  analysis  begins.  But  I  believe 
that  careful  psychological  study  of  the  thinking  process  would 


T  Cf.  Bradley,  Principles  of  Loiiic,  p.  447.  "Unawares  then  we  strive 
to  realize  a  completion,  single  and  self-contained,  where  difference  ami 
identity  are  two  aspects  of  one  process  in  a  self-same  substance,  and 
where  construction  is  self-(liremi)tion  and  analysis  self-synthesis.  This 
idea  of  system  is  the  goal  of  our  thoughts. ' ' 


162  FOOTNOTES  TO  FOBMAL  LOGIC 

show  that  we  often  reverse  the  process  several  times  in  a  single 
judgment.  We  find  an  analogy  in  the  physical  world  in  the 
solution  of  the  familiar  Japanese  puzzles.  We  often  take  out 
several  sticks  and  then  restore  them  to  their  respective  positions 
in  order  to  make  sure  that  we  may  in  the  end  bring  the  pieces  all 
together  again.  So  too,  in  pursuing  an  unknown  path  through 
the  woods,  we  glance  back  often  over  our  shoulders  in  order  that 
the  path  may  be  familiar  on  the  return  journey. 

As  I  have  already  remarked,  of  all  our  English  synonyms  for 
analysis  and  synthesis,  differentiation  and  construction,  or  inte- 
gration seem  best  to  bring  out  the  reversible  and  transitive  char- 
acter involved.  Any  process  of  genuine  construction,  always 
exhibits  the  final  whole  in  and  through  its  parts,  as  many  genera- 
tions of  idealists  from  Plato  to  Hegel  have  taught.  It  is  both 
analytic  and  synthetic,  therefore  not  just  idle  nor  yet  false. 

Among  the  various  attempts  to  preserve  for  analysis  and  syn- 
thesis separate  and  entirely  independent  functions,  that  which 
rests  upon  the  distinction  l)etween  ground  and  consequence  has 
had  many  defenders."^  It  is  maintained  that  whenever  thought 
follows  out  a  premise  to  a  conclusion,  or  passes  from  cause  to 
effect,  the  process  is  synthetic.  But  when  the  movement  is  in 
the  reverse  direction,  namely,  from  consequence  to  ground,  or 
effect  to  cause,  the  process  is  analytic.  But  obviously  this  view 
presupposes  a  transformation  of  the  judgment  in  which  its  essen- 
tial non-temporal  character  is  disregarded.  The  relation  of  cause 
to  effect,  of  ground  to  consequence,  is  a  transitive  and  reversible 
relation.  This  reciprocal  relationship  is  the  vital  characteristic 
of  inference  and  judgment,  and  even  of  conception.  In  the 
relation  of  cause  and  effect,  the  cause  is  quite  as  much  condi- 
tioned by  the  effect  as  the  effect  by  the  cause.  This  basal  truth 
is  continually  overlooked  in  the  instrumental  theories  of  judg- 
ment. And  the  fallacy  when  carried  on  into  the  discussions  of 
mediate  inference  causes  endless  confusion. 


8  Cf .  Mellone,  Introductory  Text-Bool-  of  Logic  (ed.  2;  Loudon,  Blac-ks- 
wood,  1895),  p.  99. 


Xorh'LTV  .1X1)  IDEMITY  IS  ISl'ERKSCE  WA 

Siilijcci  iiiid  |)i'c(l icjiti',  piciiiiscs  and  conclusion,  ai'c  lixjillnv 
III  till'  mind;  on  !lii'  |>iiiitcd  |)age  they  arc  ncecssai'ily  spread  out 
seriatim.  The  proposition  and  the  syllogism  are  in  time,  but  the 
judgment  and  the  infei-ence,  of  which  they  are  the  outward 
expressions,  are  not  in  time.  The  judgment  is  not  transition 
from  subject  to  predicate,  noi-  is  the  inference  a  transition  from 
pi'cnuse  to  conclusion.  The  parts  of  the  judgment  do  not  follow 
t'acli  other  like  the  ])arts  of  the  projjosition.  The  relation  is  not 
iiKTely  h(  I ic((  II  two  iiieiitid  states,  l)nt  is  icilhiti  a  single  enwhol- 
iiit^-  menial  state.  This  siii,t,de  i(h'a  within  wiiieh  tlie  elements  of 
the  jndgment  are  iield,  not  only  permits  l)Ut  compels  a  transitive, 
reversible  relationshi])  between  those  parts.'' 

The  presented  facts  wliich  constitute  the  subject  in  the  judg- 
ment contain  two  groups  of  elements,  those  which  are  explicit 
in  the  prinuuy  apprehension  or  perception  and  those  which  are 
imi)licit.'"  Now  the  analytic  judgment,  is  on  the  one  hand, 
overt  1\-  the  e.\})licati()n  of  these  implications,  and,  on  the  other 
side,  tacitly  the  syntlu'sis  of  these  same  elements.  The  word 
analytic  with  its  usual  connotations  as  I  have  pointed  out,  is 
incompetent  to  exhibit  this  redintegration  in  the  so-called  analytic 
judgment — overt  introspection  (inward  looking)  with  tacit  retro- 
spection (outward  looking).  We  likewise  discover  in  the  syn- 
thetic judgment  the  same  essential  dual  process.  The  only  diifer- 
enee  here  is,  that  the  group  of  presented  facts,  which  again  takes 
its  ])lace  as  the  sul)ject  in  the  judgment,  is  now  seen  to  be  a  con- 
stituent element  of  the  whole  which  in  the  primary  apprehension 
was  implied.  This  larger  whole  now  becomes  inijilicit ;  it  is  dis- 
covered  that    the   subject    which    in    the    pi'iinary    ai)prehension 


"  This  is  the  now  familiar  doctrine,  so  long  and  so  ably  defended  by 
Bosanquot.  The  essential  conconiitancy  of  the  parts  of  judgment  had 
of  course,  been  ])ointed  out  many  times  before,  in  the  history  of  Logic, 
but  no  one  had  ever  insisted  u]ion  the  |)rinci{)le  with  such  rejieated 
emphasis. 

10  7t  must  be  admitted,  of  course,  that  there  is  some  difliculty  in 
speaking  of  these  elements  as  being  implied  in  the  original  datum.  The 
enormously  complicated  (juestion  of  the  meaning  of  implies  is  here  involved. 


164  FOOTNOTES  TO  FOBMAL  LOGIC 

seemed  single  and  isolated  is  in  reality  correlated  with  at  least  one 
other  group  of  elements  into  a  larger  concept,  or  idea.  Thought 
is  continually  bringing  together  at  one  moment  the  result  of  the 
abstraction  of  a  previous  moment.  Thought  begins  with  a  whole 
— with  reality  in  some  sense  grasped  as  an  entirety.  It  then  pro- 
ceeds to  disperse  this  whole  by  analysis  (not  a  complete  dispersion 
however)  and  then  gathers  the  dispersed  elements  into  a  whole. ^^ 
We  first  ' '  grasp  the  sorry  scheme  of  things  entire, ' '  then  ' '  shatter 
it  to  bits"  and  finally  "remold  it  nearer  to  the  heart's  desire." 
A  vital  question  now  arises  which  Professor  Dewey  asks  as 
follows:^-  "Why  and  how  should  perfect,  absolute,  complete, 
finished  thought  find  it  necessary  to  vSubmit  to  alien,  disturbing, 
and  corrupting  conditions  in  order,  in  the  end,  to  recover  through 
reflective  thought  in  a  partial,  piecemeal,  wholly  inadequate  way 
what  it  possessed  at  the  outset  in  a  much  more  satisfactory  way?" 
But  no  serious  idealist  has  ever  been  willing  to  admit  that  thought 
is  as  Dewey  says,  perfect,  absolute,  complete,  and  finished,  before 
it  has  submitted  to  these  apparently  alien,  disturbing  conditions 
of  judgment.  It  is  not  truly  itself  until  it  has  discovered  itself 
by  passing,  in  a  piecemeal  fashion,  through  these  seeming  foreign 
conditions.  This  reflective  process  through  which  thought  passes 
is  not  partial  and  inadequate ;  it  is  the  highest  type  of  adequacy, 
namely,  self-completing  adequacy.  You  may  try  to  condemn 
thought  by  calling  it  finite,  relative,  conditioned,  imperfect,  frag- 
mentary, since  it  is  obliged  to  reconstruct  reality  by  the  device 
of  judgment.  In  fact  thought  will  join  you  in  such  a  condemna- 
tion of  itself ;  but  forthwith  it  produces  from  within  the  principle 
of  its  own  self-perfection,  by  means  of  which  it  escapes  from  all 
of  these  self-imposed  limitations. 


11  Bradley  has  expressed  this  thought  with  his  usual  clarity  and 
vigor:  "Analysis  is  the  inward  synthesis  of  a  datum,  in  which  its  unseen 
internal  elements  become  explicit.  Synthesis  is  the  analysis  of  a  latent 
whole  beyond  the  datum,  in  which  the  datum  becomes  explicit  as  a  con- 
stituent element,  bound  by  interrelation  to  one  or  more  elements  likewise 
constituent."    Principles  of  Logic,  p.  432. 

12  Logical  Theory,  p.  45. 


\-<n  I'-.l/rV  AXD  IDEXTITY  IS  ISh  KHEXCE  KJo 

III  tills  (liscussioii  dl'  llic  cssciil  i;il  iilciitity  or  ;i1  least  the 
inscpai'abli'  coiTclativity  between  analysis  and  synthesis,  it  is 
important  to  point  out  that  the  thougiit  i)rocess  exiiibitcd  in 
the  relationship  is  one  that  always  involves  a  tnadic  i-elation.  1 
have  already  sj)ok('(i  of  the  dualilii  of  the  i-clation  bu1  iIhtc  are 
really  three  centers  of  separate  attention.  Analysis  not  only  dis- 
tinguishes each  element  from  the  other,  but  also  distinguishes 
each  element  from  the  whole.  Also,  when  we  read  off  the  con- 
tent ill  the  reverse  direction,  we  find  that  synthesis  so  combines 
parts  into  wholes  that  the  relations  of  the  whole  to  each  of  the 
several  parts,  a.s  well  as  of  the  ])arts  to  each  other  is  never  obliter- 
ated. Both  analysis  and  synthesis  establishes  ami  maintains 
relations,  but  the  relations  here  involved,  I  repeat,  are  essentially 
triadic,  because  every  such  relation  involves  both  a  between  and 
a  within.  If  the  relations  between  two  terms  ^4  and  B,  be 
expressed  by  R,  then  1\'  would  exjiress  the  whole  within  wliieh 
this  relation  is  embedded,  and  R,  the  relation  between  A  and  M 
and  also  between  B  and  M.  The  triadic  relationship  would  run 
thus:  A-R-B,  A-R-M,  B-R-M.  While  it  is  true  that  every 
judgment  is  both  analytic  and  synthetic,  we  may  yet  assert 
(without  yielding  any  essential  part  of  the  position  we  are 
advancing),  that  judgments  of  sense  are  synthetic  and  judgments 
of  reason  are  analytic.  The  former  do  transcend  the  sense-pre- 
sented content;  they  are  more  than  simple  apprehension.  The 
latter  always  start  with  a  whole  or  system,  in  which  differences, 
already  existing  are  further  developed. 

Some  writers  have  attempted  to  overcome  the  apparently 
vitiating  tautology  of  the  analytic  proposition  by  making  two 
classes  of  so-called  verbal  proposition — analytic  and  synon- 
omous.^^  In  the  one  class  the  predicate  aims  at  an  exposition, 
or  analysis  of  the  intension  of  the  subject,  for  example,  Bodies 
are  extended.  An  equilateral  triangle  is  a  triangle  having  three 
equal  sides.    These  are  regarded  as  the  true  type  of  what  should 


13  Cf.  Keynes,  Formtil  Lntjir,  p.  50. 


166  FOOTNOTED  TO  FOEMAL  LOGIC 

be  called  analytic  pi'opositions.  They  are  never  tautologies  or 
bare  identities  and  therefore  may  never  be  condemned  as  trivial. 
Even  where  the  exposition  of  the  intension  of  the  subject  is  com- 
plete and  the  proposition  becomes  a  definition,  such  propositions 
are  still  to  be  distinguished  from  the  other  group  which  Keynes 
calls  "synonymous."  In  this  class  the  predicate  is  not  an  exposi- 
tion of  the  intension  of  the  subject ;  it  gives  information  only  in 
regard  to  the  external  reference  of  the  subject  or  is  its  dictionary 
synonym,  for  instance,  Tnlhj  is  Cicero,  or  A  story  is  a  tale.  This 
is  a  distinction  that  for  practical  purposes  may  be  useful,  but  it  is 
hardly  defensible  theoretically.  The  class  of  synonomous  propo- 
sitions that  is  here  interpolated,  is  provided  with  no  precise  line 
of  logical  demarcation  from  the  analytic  and  the  synthetic  class. 
A  third  class  is  not  strictly  needed.  Even  in  those  propositions 
where  subject  and  predicate  are  both  singular  terms  we  may, 
and  in  truth,  must  regard  the  judgment,  which  the  proposition 
expresses  as  an  equating  of  synonyms,  as  conforming  to  the  funda- 
mental principle  of  all  judgment,  namely,  the  assertion  of  an 
identity  in  difference.  Neither  in  judgment  nor  in  inference 
can  thought  pass  from  particular  to  particular ;  for  example  the 
proposition  this  is  that  corresponds  to  no  actual  judgment  anj' 
more  than  this  is  this.  We  do  violence  to  the  real  judgment  when- 
ever we  attempt  to  interpret  it  in  any  other  way  than  that  of  a 
universal,  exhibiting  itself  in  and  through  its  differences.  The 
challenge  to  describe  these  synonomous  propositions  as  either 
analytic  or  synthetic  can  not  be  met,  indeed,  if  it  means  that 
they  are  to  be  either  one  to  the  exclusion  of  the  other.  But  they 
can  all  be  described  as  analytic-synthetic.  Even  Tulhj  is  Cicero 
or  A  story  is  a  tale  are  assertions  of  identity  in  the  midst  of  a 
difference ;  we  pass  out  beyond  the  judgment  at  the  one  link  into 
bare  tautology  and  at  the  other  into  falsity. 

The  results  on  which  we  would  insist  may  now  be  briefly 
summarized.  The  relation  of  judgment  to  conception  is  recip- 
procal.    The  judgment  expands  the  conception  and  in  expanding: 


NOVELTY  AM)  IDESriTY  IX  ISFEBENCE  Ki? 

enriclics  ils  iiicaniiit^.  It  docs  lliis  tj\'  aililiii<^  lu-w  [•datioiis  to  tin- 
gi-oup  of  references  that  it  already  has.  Evci-y  judgment  asserts 
botli  identity  and  difference.  An  a.ssertion  that  is  merely  identical 
is  no  judgment.  So,  too,  if  a  judgment  is  merely  .synthetic,  and 
no  bond  is  perceived  between  the  subject  and  predicate,  that  is,  if 
the  two  ai'e  not  seen  to  l)e  ein])edded  within  a  whole  there  is  no 
real  judgment,  but  only  association.  Every  judgment  purpoits 
to  be  both  a  unity  and  a  multiplicity.  If  it  did  not  fulfil  its 
puipose  to  exhibit  an  identity,  it  would  cease  to  exi.st.  Hut  this 
external  unity  at  which  it  aims  is  not  inconsistent  with  endless 
multijilicity  within.  The  content  of  judgment,  though  a  single 
definite  idea  in  any  external  reference,  is  when  viewed  interiorly, 
capable  of  manifest iiig  itself  in  an  endless  vai'iety  of  meanings. 
Judgment  is  a  self-enclosing  expansion,  a  unifying  of  the  many 
and  a  multiplying  of  the  one.  The  reality  with  which  judgment 
is  concerned  is  a  whole,  completely  revealing  itself  in  each  of  its 
parts.  Judgment  is  a  units-  bi-eaking  itself  up  into  a  multii)iieil\' 
and  then  reasserting  itself  as  a  unity.  It  is  the  highest  type  of 
redintegration.    It  is  both  true  and  false  and  neither. 

Ill 

The  fii-st  of  all  the  preiUMpiisites  for  judgment  is  a  world  of 
realitx-  ditfei'ent  fi'om,  or  at  least  distinguishable  from  the  woi'ld 
of  ideas.  A  judgment  always  claims  to  be  true.  It  is  idle  to  talk 
about  judgment  until  we  have  distinguished  between  idea  or 
psychical  fact  and  the  reference  of  idea  to  objective  fact  or 
reality.  One  of  the  purjjoses  of  these  studies  is  to  show  how  and 
why  this  distinction  is  maile.  This  claims  to  he  tn(< .  which  is  one 
of  the  several  correlated  factors  in  all  judgment,  might  also  be 
described  as  judgment's  intrinsic  necessity.  It  would  also  be 
ecpially  accurate  to  speak  of  it  as  the  (ihjfcfirit)j  in  judgment. 
Objictiritij  in  judgment  is  nothing  else  than  its  )i( crssify.  What 
we  are  obliged  to  think,  through  this  self-compulsion  of  thought. 


168  FOOTNOTES  TO  FOSMAL  LOGIC 

constitutes  its  objectivity.  These  are  truths  that  the  history  of 
Logic  has  repeatedly  been  compelled  to  recognize.  No  one  can 
understand  thought  as  an  instrument  of  conviction  until  he  has 
studied  it  in  its  relation  to  its  subject  matter.  There  is  an  inter- 
structural  correspondence  between  thought  and  facts.^*  Everj- 
judgnient  therefore  has  objectivity  even  if  it  has  no  object.  And 
such  a  view  of  objectivity  allows  us  to  say  that  the  conditions  of 
actual  and  possible  thought  do  correspond  with  the  conditions  of 
actual  and  possible  being,  and  that,  therefore,  what  we  think 
exists  and  what  we  can  not  think  does  not  exist. 

Since  judgment  always  refers  to  something  other  than  itself, 
it  has  been  maintained  that  Logic  is  the  science  of  thought  when 
engaged  upon  an  object  other  than  Logic.  This  is  a  doctrine 
which  I  think  is  entirely  defensible  although  the  common  under- 
standing of  it  leads  to  all  manner  of  contradictions.  The  living 
judgment,  perhaps,  can  not  become  its  own  object  and  still  live. 
The  Hegelians  have  always  held  that  immediate  consciousness  is 
self-contradictory.  For  them  there  is  no  such  thing  as  the  vivi- 
section of  a  thought.  But,  continuing  this  metaphor,  may  we 
not  say  that  there  can  be  a  postmortem  examination  of  departed 
thinking  by  its  own  resurrected  self  ? 

The  attempt  to  make  a  distinction  between  the  judgment  of 
perception  and  cognitive  judgment  breaks  down  with  any  care- 
ful analysis  of  psychical  facts.  There  is  no  difference  in  kind, 
on  our  theory,  between  perceiving  and  perceiving  that  I  per- 
ceive, or  between  thinking  and  thinking  that  that  is  one  of  my 
thoughts.  Idealism  of  every  form  declares  that  objects  of 
thought,  just  because  they  are  thought,  have  a  different  kind  of 
existence  from  what  belongs  to  them  when  they  are  not  thought — 
if  that  may  ever  be.  Mind  is,  in  other  words,  in  some  sense 
creative.  The  realist  says  that  the  validity  of  thought  depends 
quite   as  finally   upon   the   object   thought    about,    as   upon   the 


14  On  this  point  we  are  in  eordial  agreement  with  the  instrumental 
pragmatist;  we  differ,  as  I  have  tried  to  point  out  in  an  earlier  chapter, 
on  the  wav  in  which  the  relation  is  read  off. 


NOVELTY  .IM)  IDKSTITY  IN  IN FK HENCE  1(59 

tliouglit  itself.  lie  f(jiitcn(l.s  for  a  fuiulanit'iital  distinclioii 
between  idea  and  object.  He  grants  the  idealist's  main  conten- 
tion that  ccrlaiii  objects  of  thought  do  not  exist  outside  of  the 
mind,  l)ut  he  denies  that  therefore  tlie  mind  creates  these  objects. 
When  redueeil  to  its  h)west  terms  and  stripped  of  all  unnecessaiy 
vei'hiage,  lliei-e  is,  one  fundamental  difference  between  the  old  and 
new  Logic.  Every  form  of  idealism  has  asserted  that  experience 
does  create  its  object,  that  the  self  does  beget  the  not-self. 

I'rofessor  Dewey'"'  has  stated  in  a  very  concise  form  what  he 
takes  to  l)e  "the  point  of  contact  and  hence  of  conflict"  between 
idealism  and  insti-umentalism.  The  significant  sentence  reads: 
"The  idealistic  logic  started  from  the  distinction  between  imme- 
diate plural  data  unifying,  rationalizing  meanings  as  a  dis- 
tinction ready  made  in  experience,  and  it  set  up  as  the  goal  of 
knowledge  (and  hence  as  the  definition  of  true  reality)  a  com- 
plete, exhaustive,  eomprehensive,  and  eternal  system  in  whieh 
plural  and  iniincdiate  data  are  foi'ever  woven  into  a  fabric  and 
pattern  of  self-luminous  meaning.''  A  liberal  idealist  could 
accept  this  statement  by  changing  the  one  word  *' self-luminous" 
to  "self  illuminating."  This  would  make  the  difference  between 
static  and  dynamic  idealism.  Thought  is  not  perfect  but  self- 
perfecting.  Thought  strives  for  something;  it  needs  something 
apparently  beyond  itself;  it  is  permeated  with  wonder,  with 
curiosity,  which  points  to  a  fundamental  defect  in  its  nature. 
But  in  this  never-ending  aim  to  be  a  whole,  to  be  self-complete. 
thought  is  incessantly  discovering  tluit  there  is  nothing  genuinely 
outside  of  itself.  If  in  this  striving  for  self-comi)leteness,  it 
should  actually-  I'caeli  its  goal,  thought  as  sueli  would  obviously 
be  destroyed.  Thought's  aim  is  to  get  hold  of  an  object  as  a 
whole,  the  separate  elements  of  which  it  already  has.  Now  it  is 
precisely  this  self-completion  of  thought  beyond  itself,  which 
constitutes  the  ol)jeet,  the  independent  thing  in  every  type  of 
realism.     In  the  subject-object  relation,  then,  the  expected  self- 


15  Experiinontal  Lo^jic,  ji.  22 


170  FOOTNOTES  TO  FORMAL  LOGIC 

tra)iscendcnci)  of  tJie  suhjcct  constitutes  the  object.  Thought 
moves  by  means  of  relations  toward  a  goal  which  lies  beyond 
relations.  The  attainment  of  its  goal  by  transcending  relations 
would  be  the  annihilation  of  thought. 

Wliat  Idealistic  Logic  discovers  when  it  reaches  final  reality 
is  a  whole  in  which  distinctions  can  be  made  and  are  made,  but 
in  which  the  genuine  diversit}' — the  bona  fide  independence — 
demanded  by  the  New  Realism  does  not  exist.  The  position  of 
modern  realism  on  this  central  question  of  Logic  can  be  stated 
briefly,  but  with  rough  justice  thus :  The  perception  of  relations, 
which  is  the  fundamental  characteristic  of  the  judging  conscious- 
ness, is  a  self-contradictory  but  necessary  blending  of  the  one 
and  the  many,  unity  and  variety.  This  relation  is  unique, 
logically  indefensible  and  undefinable.  Consciousness,  it  is 
asserted,  has  the  undeniable  feature  of  immediacy.  The  idea 
has  hold  of  its  object.  This  establishes  continuity.  But  equally 
undeniable  is  the  characteristic  of  self-dependence,  or  independ- 
ence. The  terms  which  consciousness  unites  in  the  relating 
activity  of  judgment  are,  in  truth,  given  to  it.  and  not  actually 
made  by  it.  This  given  reality"  with  which  it  deals  is  therefore 
essentially  pluralistic. 

But  I  submit  that  at  this  point  the  modern  realist  has  allowed 
his  dialectic  to  halt.  He  has  stated  only  half  of  the  whole  truth. 
The  other  half  is  the  indisputable  fact  that  this  cognition  which 
binds  together  the  many,  represents  at  its  center  an  original 
underived  whole.  It  is  a  synthesis,  a  unity,  which  is  not  made 
by  the  original  differences  in  the  presented  facts,  but  is-  placed 
upon  them.  The  whole  is  not  just  composed  of  its  parts,  it  con- 
stitutes them  and  is  legislatively  sovereign  over  tliem.  Now  it  is 
this  characteristic  and  apparently  paradoxical  feature  of  thought 
that  neither  the  Instrumental  Logic  nor  the  analytic  realism 
seems  able  to  surmount.  Thought  does  aim  to  retain  these  two 
features,  unity  and  plurality,  and  at  the  same  time  weld  them  into 
a  higher  harmonv.     It  strives  to  reach  an  all-embracing  whole 


NOrn/.TY  .IM)  IDKSTITY  IX  I S F IIUESCK  171 

wliich  shall  not  in  any  way  contlict  with  thi-  iiiniiediate  elements. 
It  therefore  bestows  upon  its  elements  a  kind  of  independence. 
But  at  the  same  time  it  seeks  for  elements  that  shall  Ix*  sul)- 
ordinated  to  the  entirely  independent  (i.e.,  suju'rior )  whole. 

There  is,  then,  this  i)arado.\ical  fact  a))0ut  thought  and  its 
object;  they  are  two  and  yet  can  never  be  studied  in  isolation. 
Thinking,  is  always  thinking  about  something,  and  thought  can 
never  be  divorced  fi-niii  tliis  postiUated  objectivity  and  treated  as 
pure  subjectivity.  This  poiiil.  whieh  has  now  so  often  been 
insisted  unon,  seems  iiivai-ial)ly  to  be  igiioi-ed  l»y  realists  and 
])ragmatists  in  tlieir  ci-iticism  of  idealism.  Thought  can  never  be 
investigated  in  abstraction  from  its  objective  reference.  Such 
a  view  as  I  am  here  stating,  concerning  the  relation  of  subject 
to  object,  may  when  taken  at  its  face  value,  appear  to  be  a  con- 
cession to  the  centi-al  thesis  of  pragmatic  logic,  namely,  that  the 
form  of  thought  must  wait  upon  its  matter.  On  this  view,  it  will 
be  asked,  how  can  Logic  be  regarded  as  the  study  of  the  forms 
of  thought?  If  the  form  and  the  matter  are  thus  inseparable, 
inter-related,  in  each  concrete  instance  of  thought,  how  can  there 
be  any  form  in  general?  I  cannot  think  the  answer  to  these 
questions  and  the  justification  of  Formal  Logic  is  far  to  find. 
Just  as  we  can  incpiire  into  the  laws  of  gravitation  without 
examining  all  the  objects  that  have  ever  fallen,  so  we  may  study 
the  laws  of  thought  without  studying  all  the  objects  that  may 
conceivably  be  discovei-ed  at  the  otlier  end  of  the  siibject-object 
I'clation. 

IV 

TluTc  now  arises  a  question  of  singular  gravity,  the  central 
question  of  speculative  Logic  through  all  the  centuries.  That 
portion  of  thought's  content  which  constitutes  its  meaning  or 
external  reference  as  distinguished  from  its  existence,  we  have 
insisted,  is  a  systenuitic  totality.  This  is  wliat  we  mean  when 
we  speak  of  the  woidd  of  all  possible  objects  of  thought.     How 


17-2  FOOTNOTES  TO  FORMAL  LOGIC 

far  into  this  realm  of  objective  reference  must  thought  go  before 
it  can  claim  finality  for  its  deliverance  ?  One  school  of  philosophy 
has  held  that  perfect  validity  of  thought  would  require  perfect 
insight  into  the  objective  system.  Bosanquet  has  said,  "Ulti- 
mately nothing  can  be  rightly  known  without  knowing  all  else 
rightly. ' '  Others  insist  that  we  have  some  knowledge  that  is  in- 
complete and  yet  perfect,  and  that  we  can  pronounce  judgments 
that  are  not  subject  to  future  revision.  The  agnostics,  from  the 
ancient  sophists  to  the  new  realists  have  declared  that  never  in 
the  growth  of  knowledge  do  we  reach  a  stage  at  which  we  may 
say,  "The  evidence  is  now  all  in,  and  the  judgment  of  finality 
can  be  pronounced.  We  do  not  have  perfect  control  over  the 
object ;  if  we  did  it  would  cease  to  be  an  object.  It  is  just  this 
alien  character  that  constitutes  its  objectivity. 

The  Idealists  have  always  given  a  decisive  affirmative  answer 
to  this  fundamental  question ;  we  do  have  perfect  knowledge  in 
part.  Professor  Hocking  has  defended  this  cardinal  tenet  of 
traditional  idealism  with  impressive  clarity  of  illustration.  He 
pointedly  tells  us  that  unfinishedness  is  not  itself  a  blemish,  and 
says:  "There  are  tolerable  and  intolerable  kinds  of  unfinished- 
ness. A  thing  is  properly  unfinished  when  it  is  finishable ;  and 
it  has  an  identity  that  finishing  will  not  change.  Let  an  artist 
sketch  a  face  with  all  conceivable  haste  and  roughness.  The 
unfinishedness  is  justified  if  only  it  is  a  thing,  if  only  it  has  a 
character  and  a  significance  that  all  later  finishing  does  but 
develop  without  displacement  or  substitution."^" 

The  truth  about  our  fragmentary  thought,  as  it  comes  to  us 
by  the  pathway  of  experience,  is  not  that  it  is  imperfect  or  incon- 
sistent, but  that  it  is  incomplete.  It  is  indeed  not  adequate  to  the 
whole  of  reality,  but  what  it  does  deliver  is  genuine.  From  its 
one  shore,  thought  bridges  the  gulf  between  it  and  reality  by 
pushing  out  cumulative  cantilever  arches,  each  firmly  and 
unchangeably  anchored.     It  is  not  a  pontoon  bridge  whose  units 


i«  The    Meaning    of    Go<l    in    Human    Experience    (New    Haven.    Yale 
University  Press,  1912),  p.  x. 


S(>]'i:i/rY  AM)  h)F.STirv  IS  isfi:i;i:s(:e  \~:\ 

ai'c  swayiMl  l»y  ihc  dasliiiij^  tide,  and  wiiosc  mooring  to  the  shore 
may  fciiuiic  to  Ix-  clianged  as  its  lengtli  iiic-i-cases. 

Actuality,  which  is  just  one  aspect  of  objectivity,  is  the 
necessitated  possible.  This  is  Bradh^y's  well-known  view.  The 
most  fundamental  law  of  tliought  is  the  law  by  which  we  assume 
that  every  isolated,  unii|ue  possibility  is  also  I'cal.  In  oIIh-i- 
words,  the  iiHconil^(ilf((l  possible  is  the  actual.  This  law,  <'annot 
be  exhibited  as  the  operation  of  either  analysis  or  synthesis  oi- 
both  correlated,  and  yet  it  is  a  normal,  universal  way  of  thought  *s 
functioning.  Evei-y  time  i-eality  presents  itself  as  a  subject  for 
a  possible  judgment,  and  i-eaehes  out  among  the  possible  predi- 
cates, that  one  of  these  possil)le  jjredieates  which  finally  .stands 
alone,  either  because  tliere  ai'e  no  other  jjossible  predicates,  or 
because  other  competing  possibilities  have  been  rejected,  is  appro- 
priated by  the  subject.  This  appropriation  elevates  the  predicate 
from  possibility  to  actuality.  We  may  not  be  cognizant  of  the 
operation  of  tliis  Uiw.  and  may  indeed  when  our  attention  is 
directed  to  its  opei'ation,  l)e  inclined  to  disclaim  it,  but  we 
nevertheless  do  finally  and  always  owe  allegiance  to  it.  Insteatl 
of  saying  that  the  mind  selects  one  of  the  several  alternatives 
and  so  depresses  llie  olliers.  it  would  be  moi-e  accurate  to  say 
that  the  several  impossible  possibilities  having  been  destroyed 
the  single  uneombatted  possibility  stands  self-affirmed.  The 
actual,  the  real,  the  object,  is  that  which  resists  the  subject.  A 
thing  has  objectivity  if  it  exhil)its,  in  its  own  name,  any  force 
or  necessity. 

This  doctrine  again  must  not  l)e  confused  with  tlie  teaching  of 
pragmatic  Logic,  which  at  first  sight  it  resembles.  The  Logic 
of  Pragmatism  tries  out  the  various  possibilities  and  tests  truth 
by  acting  as  if.  When  the  question  arises  whether  the  new 
possibilities  which  are  applying  for  acceptance  are  true,  or  real 
we  must  test  them,  one  by  one.  by  acting  as  if  they  were  time, 
and  accept  in  each  instance  tlu)se  that  work  in  witii  the  old.  But 
this  pragmatic  test  of  ti-uth.  as  I  have  shown  elsewhere,  assunu's 


174  FOOTNOTES  TO  FOBMAL  LOGIC 

the  rationality  of  the  old,  and  asserts  that  the  new  which  works 
in  with  this,  is  true.  Of  course,  if  we  start  with  an  original 
matrix  of  truth,  then  whatever  this  accepts  as  true,  will  be  true, 
and  whatever  it  rejects  because  it  does  not  work,  will  be  false. 
But  the  Pragmatic  Logic  is  incapable  of  endowing  this  original 
mass  with  the  essential  truth  necessary  to  make  the  principle 
as  if  operate.  Bradley's  doctrine  does  on  the  surface  seem 
identical  with  the  pragmatic  test — wherever  a  suggestion  is  not 
rejected  by  the  facts  with  which  we  start,  or  again  l)y  some  other 
suggested  quality,  and  we  are  left  not  with  disparate  possibilities, 
but  with  one  loicomhattrd  maijhe,  that  suggestion  must  always 
be  taken  as  fact.  The  facts  with  which  the  pragmatist  starts  are 
not  possessed  of  universality ;  with  Bradley  they  are.  He  says : 
"The  striving  for  perfection,  the  desire  of  the  mind  for  an 
infinite  totality  is  indeed  the  impulse  which  moves  our  intellect 
to  appropriate  everything  from  which  it  is  not  forced  off." 
Possibility  is  a  kind  of  necessity,  and  consequently  there  is  no 
difference  in  kind  between  the  problematic  and  the  apodeictic 
judgment.  A  thing  is  possible  when  at  least  one  of  its  conditions 
is  present,  and  actual  when  none  of  its  conditions  is  absent. 


V 

As  a  typical  illustration  of  the  sceptical  attitude  of  the  new 
movement  toward  reality,  objectivity,  or  necessity,  we  may  quote 
two  Protagorean  passages  from  Professor  Sidgwick:  "Absolute 
truth  is  never  attained  but  that  further  improvement  is  always 
possible. "  "  There  is  no  need  to  make  any  pretence  of  securing 
infallibility  of  judgment,  even  in  a  single  instance.  If  Absolute 
Truth  means  Truth  as  it  would  appear  to  a  superhuman  mind, 
how  can  we  presume  to  have  reached  it?  Or,  if  by  any  chance 
we  did  reach  it,  what  means  would  we  have  of  distinguishing 
between  it  and  the  truth  that  merely  suffices  for  human  pur- 
poses?"''    The  modern  idealist  always  replies  to  this  agnosticism 


3"  Elementary  Logic,  pp.  123,  170. 


NOVELTY  A\l)  IDESTITY  IS   I S FEIIENCE  17.1 

ill  tlic  spii'it  of  Soei'atcs'  fcply  to  tlif  iiinMcnt  sceptics.  Knowl- 
edge has  tliis  pcculiaf  pai'adox  al)oiit  il  :  We  have  a  criterion 
of  truth — we  know  what  valid  knowledge  ought  to  be;  and  yet 
we  can  never  in  our  practical  experience  reach  any  such  knowl- 
edge as  is  guaranteed  by  this  criticism  of  validity. 

Professor  Sidgwiek's  own  statcinciil  lliat  "ahsolulc  li-iitli  is 
never  attained  but  tluit  further  iin|)roveiiient  is  always  possible'' 
is  itself  an  illustration  of  this  "self-perfecting"  critei-ion  of 
knowledge.  When  we  assert  that  further  improvement  is  possible, 
we  imply  a  criterion  of  stable  values,  or  else  the  word  improve 
ment  does  not  mean  what  it  purports.  Improvement  and  pro- 
gress ai"e  indeed  dignified  woi'ds  but  no  one  has  any  right  to  use 
llieiii,  eitlici'  in  Logic  or  p]tliies,  who  does  not  admit  something 
absolute,  some  definable  standards  of  value.  The  modern  enemy 
of  Traditional  Logic  and  Ethics  declares  that  knowledge  is 
limited  to  a  world  of  comparatives,  whose  superlatives  are  never 
in  sight.  We  do  not  know  the  beautiful,  the  true,  the  right,  and 
never  can  know  them,  foi'  there  are  no  esthetic,  logical,  or  ethical 
standards.  We  simply  have  knowledge  of  the  first  two  degrees, 
namely,  the  good  and  the  belter:  and  fi'oiii  these  as  a  base  we 
must  triangulate  our  journey.  But  in  full  view  of  all  the  many 
indictments  the  idealist  still  asserts,  with  renewed  emphasis, 
that  any  genuine  improvement  imjdies  direction,  a  goal.  If  we 
are  in  the  least  degree  uneei'tain  about  tlie  goal,  we  nnist  in  the 
same  degree  be  uncertain  about  the  improvement.  Improvement 
is  not  measured  in  terms  of  mere  moveuKMit.  We  can  be  much 
"on  the  go"  without  making  any  iiuitrovement — witness  many 
aspects  of  oui-  i)resent  civilization.  In  other  words,  l)i'iefly, 
improvement  is  estimated  not  by  tln'  distance  one  has  gone,  but 
by  the  distance  one  has  yet  to  go. 

"Tliere  are  probably  few  people  at  the  i)resent  day."  says 
Sidgwick.  "who  would  confess  to  holding  that  the  general  rules 
by  which  our  thoughts  and  our  lives  are  mostly  guided  deserve 
to  be  applied  tlirougli  tliiek  and  tliin."'^     One  may  agree  with 


i^  Elementary  Loyie,  pp.  160,  IGl. 


176  FOOTNOTES  TO  FOBMAL  LOGIC 

this  statement  so  far  as  the  word  "mostly"  is  concerned,  and 
admit  that  humanity  does  depend  for  its  practical  faiths  very 
largely  upon  insights  that  are  transitory,  partial  and  for  the 
most  part  subconscious.  We  act  most  often  before  the  arrival 
of  certainty  and  under  the  guidance  of  shifting  standards.  But 
surely  Professor  Sidgwick  must  believe  in  some  things  that  abide. 
Can  the  solemn  agreements  among  men  never  be  final  ?  Is  there 
no  pact  that  deserves  to  be  applied  through  thick  and  thin?  If 
not,  then  the  most  pragmatically  consistent  of  the  nations  in  the 
great  world-war  is  Germany.  A  treaty  is  indeed  merely  a  scrap 
of  paper  to  be  respected  only  so  long  as  it  is  convenient  to 
respect  it. 

Another  illustration  of  how  the  pragmatist  fails,  it  seems  to 
me,  to  grasp  the  idealistic  notion  of  a  self-perfecting  control  of 
the  object,  I  may  quote  from  Mr.  H.  0.  Knox:  "We  simply 
deprecate  as  futile  the  assuming  of  a  transcendent  and  absolute 
reality  as  the  standard  to  which  our  actual  judgments  are  to 
correspond.  For  (a)  if  an  absolute  standard  were  available  for 
actual  comparison  the  comparison  itself  would  be  purely  super- 
fluous. We  should  already  be  dc  facto  in  possession  of  absolute 
and  infallible  certitude.  And  (6)  to  say,  that  reality  is  trans- 
cendent is  simply  to  say  that  it  is  not  available  as  a  standard  at 
all"^^  This  is  clearly  a  restatement  of  the  ancient  paradox  of 
the  apparent  futility  or  idleness  in  judgment  which  I  have 
attempted  to  answer  in  the  chapter  on  "Tlie  Import  of  Judg- 
ment. ' ' 

All  necessity  is  in  the  end  conditional,  since  every  must  he 
rests  back  upon  a  hccausr.  All  objectivity  is  in  the  end  sub- 
jectivity since  reality  is  continuous  and  since  the  thinking  self 
(apud  Cartesianism)  is  the  initial  indefeasible  reality.  If  the 
object  lay  genuinely  outside  the  system  of  thought  it  could  never 
be  reached  by  thought.  The  knowing  process  does  not  involve 
a  transition  from  subject  to  object ;  it  consists  in  a  progressive 


i^Mind,  n.  s.,  XVIII  (1909),  602. 


yoVEl.TV  AND  IDESTITY   IS  ISFEIiENCE  177 

analysis  and  (Icvclopiiicnt  ol'  tlic  olijcctivt^  aspect  of  the  total  con- 
tinuous reality.  Tliis  view  will  seem  to  I'csciiihle  Professor 
Dewey's  account  of  the  subj( ct-ohjt tt  I'clation.  He  writes:  "The 
distinction  between  snl)jcetivity  and  objectivity  is  not  one 
between  meaning  as  such  and  datum  as  such.  It  is  a  specifica- 
lion  tluit  enici'ges,  correspondcntly,  in  both  datum  and  ideatum, 
as  affairs  of  the  direction  of  loj^-ical  movement."-"  There  is, 
however,  an  essential  difference  between  this  position  and  that 
wliich  I  have  now  ui'ged  from  sevei'al  jioints  of  view  in  these 
pages.  A  cross-section  of  the  stream  of  consciousness  in  Pro- 
fessor Dewey's  doctrine,  it  seems  to  me,  does  not  raise  the  vital 
(juestion  of  the  correspondence  or  coherence  in  the  longitudinal 
section  of  the  thinking  process.  No  matter  how  completely  we 
may  seem  to  explain  the  subject-o])ject  in  any  situation  as  the 
meeting  point  of  converging  forces,  we  still  need  the  help  of  a 
principle  outside  of  the  pragmatic  movement  to  explain  the 
identity  that  persists  in  the  spatial  or  temporal  series.  Spatial 
judgments  are  far  from  being  as  particular  or  factual  as  on  the 
surface  they  appear  to  be.  Every  here  contains  a  there  and 
hence  it  is  never  a  i)artieular.  Spatial  references  in  judgment 
are  always  universal.  Tliere  is  never  given  to  thought  a  genuine 
this  or  that,  but  always  tliisness  and  thatness.  We  may  say  the 
same  of  our  temporal  judgments.  It  has  justly  been  maintained 
that  every  present  includes  a  past,  and  therefore  no  temporal 
judgment  can  be  strictly  particular. 


-'^  Exixri mental  Loi/ic,  p.  oi5. 


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